Experimental analysis of the swirling flow in a Francis turbine draft tube: Focus on radial velocity component determination

The draft tube of a hydraulic turbine is the component where the flow exiting the runner is decelerated, thereby converting the excess of kinetic energy into static pressure. In the case of machine refurbishment of an existing power plant, most of the time only the runner and the guide vanes are currently modified. For financial and safety reasons, the spiral casing and the draft tube are seldom redesigned, even if these components present some undesirable behaviour. In some cases, the installation of an upgraded runner leads to a peculiar and undesirable efficiency drop as the discharge is increased above the best efficiency point value. It is found to be related to a corresponding sudden variation in the draft tube pressure recovery coefficient at the same discharge.The swirling flow exiting the runner is complex and highly turbulent. The radial velocity is rarely measured because a quite complicated measurement setup is needed. However, this velocity component is greatly needed in order to properly initialize the numerical simulations, and its influence is important in spite of its small magnitude. Velocity measurements downstream of the runner include radial component made at CREMHyG (Grenoble) by LDV, and PIV techniques are presented. An analytical formulation for this velocity component based on the formulation for the conical diffuser and on the three vortices structure is proposed and compared with measurements.     

Mitigation of flow-induced pressure fluctuations in a Francis turbine operating at the design and partial load regimes—LES simulations

High-fidelity large eddy simulations (LES) were conducted to characterize the spatial and temporal structure of turbulent flows in an industrial-sized Francis turbine while the unit operated at the design point and partial load. A pressure surge with an amplitude of 8% of the turbine head was observed at partial load while the amplitude was <1% at the design point. The vortex rope precession observed in the draft tube correlated to the amplitude and frequency of the pressure surge. Central and peripheral water injections at various volumetric rates were considered to control the flow-induced pressure fluctuations. Central injection at the 4% and 6% flow rates attenuated high amplitude pressure fluctuations by 40% and 75% respectively at partial load. At the same operating conditions, peripheral injections did not have the same desired effect. Although power generation was not changed with water injection at the design point, it was reduced by about 2.5% by central injection and 0.5% by peripheral injection at partial load, showing a water injection mitigation strategy could be applied without any penalty.     

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.     

URANS prediction of flow fluctuations in rod bundle with split-type spacer grid

Turbulent flow in a rod bundle with split-type spacer grid has been studied using Unsteady Reynolds-Averaged Navier–Stokes (URANS) approach. In the previous studies of turbulent flow in rod bundles URANS (as well as steady-state RANS) simulations predicted mean velocity profiles fairly well. However, they severely underpredicted velocity fluctuations, which is investigated in the present study. Our simulations were performed with the Shear Stress Transport (SST) turbulence model and automatic wall-treatment using OpenFOAM, an open-source CFD code. Results of URANS simulations are compared with the measurements of the MATiS-H experiment, which was performed at Korean Atomic Energy Research Institute (KAERI) in 2011–2012.The URANS predictions of velocity fluctuations have been improved by appropriately summing up fluctuations resolved by the basic URANS model and non-resolved fluctuations, which were modelled with the turbulence model. This treatment of turbulent fluctuations, which are directly measured in high-quality experiments, allows more detailed evaluation of various URANS turbulence models. It was found out that the best agreement is achieved when resolved and modelled fluctuations are assumed to be uncorrelated, which indicates that the large-scale structures in this particular flow are distinct in the spectral space from the rest of turbulence. Turbulent flow in the MATiS-H experiment was reproduced by numerous authors using different approaches and our results are among the most accurate.     

Flow analysis for a double suction centrifugal machine in the pump and turbine operation modes

A double suction centrifugal machine has been studied, both experimentally and numerically, operating as a pump and as a turbine. Experimentally, the static performance of the machine working as a pump was obtained. These measurements were compared with equivalent numerical results from a URANS calculation. As a second step, the numerical results have been exploited to get detailed information about the flow in both operating modes (pump and turbine). The main goals of the study are, first, the validation of the numerical procedure proposed and second, the possible turbine operation of the impeller, which could point out a wider working range for the machine. The first aspect is handled by detailed analysis in the pump mode, according to previous experience of the research group. The second objective is obtained by using the numerical model to explore the flow fields obtained, when working in an inverse mode. Therefore, the presented results join the use of a numerical methodology and the turbine mode of operation for a centrifugal impeller, providing insight into the flow characteristics. When working as a pump, the flow at the suction side is characterized by the existence of an inlet tongue, which tends to enforce a uniform flow for the nominal conditions. For the turbine mode, flow patterns in the impeller, volute and suction regions are carefully investigated. The influence of the specific geometrical arrangement is also considered for this operation mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical and experimental investigation on droplet dynamics and dispersion of a jet engine injector

In the case of turbine combustors operating with liquid fuel the combustion process is governed by the liquid fuel atomization and its dispersion in the combustion chamber. By highly unsteady flow field conditions the transient interaction between the liquid and the gaseous phase is of interest, because it results in a temporal variation of air–fuel ratio which leads to a fluctuating temperature distribution. The objective of this research was the investigation of transient flow field phenomena (e.g. large coherent structures) on droplet dynamics and dispersion of an isothermal flow (of inert water droplets) as a necessary first step towards a full analysis of spray combustion in real-life devices. The advanced injector system for lean jet engine combustors PERM (Partial Evaporated Rapid Mixing) was applied, generating a dilute polydispersed spray in a swirled flow field. Experiments were performed using Phase Doppler Anemometry (PDA) and a patternator to determine the droplet polydispersity, concentration maps, and velocity profiles in the flow. An important finding is the effect of large-scale coherent structures due mainly to the precessing of the vortex core (PVC) of the swirling air jet on the particle dispersion patterns. The experimental results then serve as reference data to assess the accuracy of the Eulerian–Lagrangian computations using a Large Eddy Simulation (LES), a Unsteady Reynolds-Average Navier–Stokes Simulation (URANS) and two simplified (steady-state) simulations. There, a simplified droplet injection model was used and the required boundary conditions of injected droplet sizes were obtained from measurements. Important transient effects of deterministic droplet separation observed during experiments, could be perfectly replicated with this injection model. It is convincingly shown, through extensive computations, that the resolution of instantaneous vortical structures is indeed crucial; hence the LES, or a reasonably-well resolved URANS are preferred over the steady-state solutions with additional, stochastic-type, turbulent dispersion models.     

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.     

Evaluation of an algebraic model for laminar-to-turbulent transition on secondary flow loss in a low-pressure turbine cascade with an endwall

The predictive qualities of a recently developed algebraic intermittency model for laminar-to-turbulent transition are analysed for the flow through a linear cascade of low-pressure turbine blades with an endwall. Both steady RANS (Reynolds-averaged Navier–Stokes) and time-accurate RANS (URANS) simulations are performed. The results are compared with reference LES (Large Eddy Simulation) by Cui et al. (2017, Numerical investigation of secondary flows in a high-lift low pressure turbine, Int. J. of Heat and Fluid Flow, vol. 63) and results by the local correlation-based intermittency transport model (LCTM) by Menter et al. (2015, A one-equation local correlation-based transition model. Flow Turbul. Combust., vol. 95) for laminar and turbulent endwall boundary layers at the cascade entrance. Good agreement is obtained with the reference LES and with results by the LCTM for the evolution through the cascade of the mass-averaged total pressure loss coefficient and for profiles of pitchwise-averaged total pressure loss coefficient at the cascade exit.     

Effects of Spray and Turbulence Modelling on the Mixing and Combustion Characteristics of an n-heptane Spray Flame Simulated with Dynamic Adaptive Chemistry

Accurate modelling of spray combustion process is essential for efficiency improvement and emissions reduction in practical combustion engines. In this work, both unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and large eddy simulations (LES) are performed to investigate the effects of spray and turbulence modelling on the mixing and combustion characteristics of an n-heptane spray flame in a constant volume chamber at realistic conditions. The non-reacting spray process is first simulated with URANS to investigate the effects of entrainment gas-jet model on the penetration characteristics and fuel vapor distributions. It is found that the droplet motion near the nozzle has significant influence on the fuel vapor distribution, while the liquid penetration length is controlled by the evaporation process and insensitive to gas-jet model. For the case considered, both URANS with the gas-jet model and large eddy simulations can properly predict the vapor penetration. For the combustion characteristics, it is found that LES yields better predictions in the global combustion characteristics. The URANS with gas jet model yields a comparable flame length and lift-off-length (LOL) to LES, but results in a larger ignition delay time compared to the experimental data. Another focus of this work is to qualify the convergence characteristics of the dynamic adaptive chemistry (DAC) method in these transient combustion simulations, where DAC is applied to reduce the mechanism locally and on-the-fly to accelerate chemistry calculations. The instantaneous flame structures and global combustion characteristics such as ignition delay time, flame lift-off length and emissions are compared between simulations with and without DAC. For URANS, good agreements are observed both on instantaneous flame structures and global characteristics. For LES, it is shown that the errors incurred by DAC are small for scatter distributions in composition space and global combustion characteristics, while they may significantly affect instantaneous flame structures in physical space. The study reveals that for DAC application in transient simulations, global or statistic information should be used to assess the accuracy, such as manifolds in composition space, conditional quantities and global combustion characteristics. For the cases investigated, a speed-up factor of more than two is achieved by DAC with a 92-species skeletal mechanism with less than 0.2 % and 3.0 % discrepancy in ignition delay and LOL, respectively.     

High‐order detached eddy simulation,zonal LES and URANS of cavity and labyrinth seal flows

Hybrid numerical large eddy simulation (NLES), detached eddy simulation (DES) and URANS methods are assessed on a cavity and a labyrinth seal geometry. A high sixth‐order discretization scheme is used and is validated using the test case of a two‐dimensional vortex. The hybrid approach adopts a new blending function. For the URANS simulations, the flow within the cavity remains steady, and the results show significant variation between models. Surprisingly, low levels of resolved turbulence are observed in the cavity for the DES simulation, and the cavity shear layer remains two dimensional. The hybrid RANS–NLES approach does not suffer from this trait. For the labyrinth seal, both the URANS and DES approaches give low levels of resolved turbulence. The zonal Hamilton–Jacobi approach on the other had given significantly more resolved content. Both DES and hybrid RANS–NLES give good agreement with the experimentally measured velocity profiles. Again, there is significant variation between the URANS models, and swirl velocities are overpredicted. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental and numerical study on the growth and collapse of a bubble in a narrow tube

The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by a high-speed camera system. In numerical simulation, the evolution of the bubble is solved by adopting axisymmetric boundary integral equation, considering the surface tension effect. The results of experiments and numerical simulations are compared and good agreements are achieved. Both of them show that a counter-jet forms and penetrates the bubble at the end of the collapse stage, before a ring type bubble forms. Under the attraction of the tube wall due to Bjerknes force, a ring jet is generated, pointing towards the tube. On the basis of this, some physical quantities like the pressure on the tube wall and kinetic energy are calculated in a case study. The effects of tube diameters and tube lengths on the bubble’s behaviors are also investigated.     

Unsteady RANS and detached-eddy simulations of flow around a circular cylinder in ground effect

Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and detached-eddy simulations (DES) were performed of flow around a circular cylinder placed near and parallel to a moving ground, on which substantially no boundary layer developed to interfere with the cylinder. The results were compared with experiments previously reported by the authors to examine how accurately the URANS and DES can predict the cessation of von Kármán-type vortex shedding and the attendant critical drag reduction of the cylinder in ground effect. The DES, which were performed in a three-dimensional domain with spanwise periodicity imposed, correctly captured the cessation of the vortex shedding, whereas both two- and three-dimensional URANS also predicted it but at a much smaller gap-to-diameter ratio compared with the experiments. The wake structures of the cylinder predicted by the DES were in good agreement with the experiments in both large- and small-gap regimes, and also in the intermediate-gap regime, where the DES captured the intermittence of the vortex shedding in the near-wake region. Based on the results obtained, further discussions are also given to the reason why the von Kármán-type vortices in the URANS solutions incorrectly ‘survived’ until the cylinder came much closer to the ground.     

Simulation and Modelling of Turbulent Trailing-Edge Flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–ε) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Kármán vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

AQUEOUS FLOW LIMITATION IN A TAPERED-STIFFNESS COLLAPSIBLE TUBE

To find out whether the relation between flow-limited flow-rate and upstream transmural pressure was nonunique, as has been reported for air flow through a tapered-stiffness tube, and for comparison with a completed investigation of flow limitation in a uniform tube, flow limitation was observed in a tapered-stiffness tube. The tube was made by removal of material from the outside of a segment of the previous uniform tubing; thus the stiffness was on average less than that of the uniform tube. Therefore, quantitative differences in behaviour were expected, but in addition significant qualitative differences were found. Whereas in the uniform tube, large-amplitude oscillations were almost entirely confined to a transition from peak pre-collapse flow-rate to the largely pressure-drop-independent flow-limited flow-rate, the latter state here included operating points of all oscillatory types. The dramatic reduction in flow-rate at the transition was absent, and instead multiple (up to six) operating points occurred at a single value of upstream head and upstream transmural pressure. The plotting of control–space diagrams revealed a unique region of weak oscillations corresponding to the tube throat being located at an intermediate and time-varying point along the tube, with collapse as far as that point only. These oscillations were extremely variable in waveshape and frequency, often displayed intermittency, and depended sensitively on the precise operating point conditions. When in this mode, the tube upstream of the final collapse position exhibited small standing waves of area, so that up to four just-perceptible minima were seen.     

Hybrid LES-RANS: An approach to make LES applicable at high Reynolds number

The main bottle neck for using large eddy simulations (LES) at high Reynolds number is the requirement of very fine meshes near walls. Hybrid LES-Reynolds-averaged Navier-Stokes (RANS) was invented to get rid of this limitation. In this method, unsteady RANS (URANS) is used near walls and away from walls LES is used. The matching between URANS and LES takes place in the inner log-region. In the present paper, a method to improve standard LES-RANS is evaluated. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane in order to provide the equations in the LES region with relevant turbulent structures. The fluctuations are taken from a DNS of a generic boundary layer. Simulations of fully developed channel flow and plane asymmetric diffuser flow are presented. Hybrid LES-RANS is used both with and without forcing conditions.     

Numerical simulation of the fluid–structure interaction in a tube array under cross flow at moderate and high Reynolds number

The unsteady loads in a tube bundle are studied at moderate and high Reynolds number by means of URANS and hybrid (DDES) modelling. The onset of fluid-elastic instability is analysed for different structural parameters, Scruton number and reduced velocity. The simulations have been carried out with the code NSMB (Navier–Stokes Multi Block) by using turbulence modelling methods URANS and DDES (Delayed Detached Eddy Simulation). The CEA-DIVA configuration is considered for the cylinders array for an inter-tube Reynolds number 60 000. The study is carried out for a configuration of (4×5) cylinders in static conditions as well as for the vertical free motion of one of the central cylinders in one DOF (Degree Of Freedom).The inter-tube Reynolds number is 60 000. It is found that this cylinder spontaneously displays an oscillatory motion which first corresponds to Vortex Induced Vibration (VIV), associated to a lock-in mechanism for low values of the reduced velocity and secondly develops Movement Induced Vibration, MIV, for higher values of the reduced velocity. The variation of the cylinder׳s oscillations frequency, of the unsteady loads and the structure׳s displacement are studied as a function of the reduced velocity for low and high values of the Scruton number. The increase of the phase-lag between the forces and the displacement is predicted and discussed for different Scruton number values and reduced velocities.     

Three-dimensional cellular structure of detonations in suspensions of aluminium particles

Recently, we have used scarce available data on the detonation cell size in suspensions of aluminium particles in air and oxygen to adjust the kinetic parameters of our two-phase model of detonations in these mixtures. The calculated detonation cell width was derived by means of two-dimensional (2D) unsteady simulations using an assumption of cylindrical symmetry of the flow in the tube. However, in reality, the detonation cells are three-dimensional (3D). In this work, we have applied the same detonation model which is based on the continuous mechanics of two-phase flows, for 3D numerical simulations of cellular detonation structures in aluminium particle suspensions in oxygen. Reasonable agreement on the detonation cell width was obtained with the aforementioned 2D results. The range of tube diameters where detonations in $\text{ Al/O}_2$ mixture at a given particle size and concentration would propagate in the spinning mode has been estimated (these results make a complement to our previous analysis of spinning detonations in Al/air mixtures). Coupling these results with the dependencies of detonation cell size on the mean particle diameter is of great interest for the understanding of fundamental mechanisms of detonation propagation in solid particle suspensions in gas and can help to better guide the experimental studies of detonations in aluminium suspensions. It is shown that the part of detonation wave energy used for transverse kinetic energy of both gas and particles is quite small, which explains why the propagation velocity of spinning and multi-headed detonations reasonably agrees with the ideal CJ values.     

Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

Combined Influence of Strain and Heat Loss on Turbulent Premixed Flame Stabilization

The present paper argues that the prediction of turbulent premixed flames under non-adiabatic conditions can be improved by considering the combined effects of strain and heat loss on reaction rates. The effect of strain in the presence of heat loss on the consumption speed of laminar premixed flames was quantified by calculations of asymmetric counterflow configurations (“fresh-to-burnt”) with detailed chemistry. Heat losses were introduced by setting the temperature of the incoming stream of products on the “burnt” side to values below those corresponding to adiabatic conditions. The consumption speed decreased in a roughly exponential manner with increasing strain rate, and this tendency became more pronounced in the presence of heat losses. An empirical relation in terms of Markstein number, Karlovitz Number and a non-dimensional heat loss parameter was proposed for the combined influence of strain and heat losses on the consumption speed. Combining this empirical relation with a presumed probability density function for strain in turbulent flows, an attenuation factor that accounts for the effect of strain and heat loss on the reaction rate in turbulent flows was deduced and implemented into a turbulent combustion model. URANS simulations of a premixed swirl burner were carried out and validated against flow field and OH chemiluminescence measurements. Introducing the effects of strain and heat loss into the combustion model, the flame topology observed experimentally was correctly reproduced, with good agreement between experiment and simulation for flow field and flame length.