Time-accurate Turbulence Modeling of Swirling Flow for Hydropower Application

Hydraulic turbomachines have played a prominent role in the procurement of renewable energy for more than a century. Embedded in the context of general technological progress, their design for efficiency and reliability has reached an outstanding level of quality. At the design point, water turbines generally operate with little swirl entering the draft tube and no flow separations, but at off-design, at both high- and low-load, the flow leaving the turbine has a large swirling component. The present work describes the turbulence modeling of a wide range of physical mechanisms that produce pressure pulsations in swirling flows. The available knowledge about these pulsations are still far from complete. If the swirl exceeds a certain level, the flow patterns associated with the swirl dominated vortex motions vacillate. A key feature of strongly swirling flows is vortex breakdown. The vortex breakdown is an abrupt change in the core of a slender vortex and typically develops downstream into a recirculatory “bubble” or a helical pattern. The swirl motion and the helical pattern has for long been of interest to scientists and engineers who have constantly strived in reproducing the naturally occurring phenomena and take advantage of their performance enhancing effects thermal and mass transport applications. The swirl effects are usually seen as either the desired result of design or unavoidable, possibly unforeseen, side effects which comprise a forced vortex core centered around its axis of rotation. The core is due to viscous forces, increases in size with successive increases in viscosity and varies over widely dissimilar length and time scales depending on the physical context. The pulsations and their impact on the efficiency and hydraulic structures of water turbines depend on the flow rate, the velocity distribution after the runner, the shape of the draft tube, and the dynamic response of the whole hydraulic structure. The high level of unsteadiness in the flow field necessitates the utilization of advanced turbulence treatment to predict the small-scale structures. Time-accurate Reynolds-averaged Navier-Stokes (URANS) models are primarily useful for capturing large-scale flow structures, while the details of the small-scale turbulence eddies are filtered out in the averaging process. In many cases also the large-scale structures are damped by the URANS modeling, which is formulated to model all the turbulence. The quality of the results is thus very dependent on the underlying turbulence model. Better approaches should be used to handle the anisotropic and highly dynamic character of turbulent swirling flows. An extended series of turbulence models are scrutinized in this work while the main focus is on hybrid URANS-LES and LES methods. Detached-eddy simulation (DES) is a promising hybrid URANS-LES strategy capable of simulating internal flows dominated by large-scale detached eddies at practical Reynolds numbers. The method aims at entrusting the boundary layers with URANS while the detached eddies in separated regions or outside the boundary layers are resolved using LES. DES predictions of massively separated flows, for which the technique was originally designed, are typically superior to those achieved using URANS models, especially in terms of the three-dimensional and time-dependent features of the flow. Scale-adaptive simulation (SAS) is another hybrid URANS-LES method which is based on detecting the unsteadiness according to the velocity gradients in the flow field. The present work gives a thorough comparison between the different levels of unsteady turbulence modeling, applied to swirling flow and the rotor-stator interaction

Unsteady numerical simulation of the flow in the U9 Kaplan turbine model

The Reynolds-averaged Navier-Stokes equations with the RNG k-ε turbulence model closure are utilized to simulate the unsteady turbulent flow throughout the whole flow passage of the U9 Kaplan turbine model. The U9 Kaplan turbine model comprises 20 stationary guide vanes and 6 rotating blades (700 RPM), working at full load (0.71 m3/s). The computations are conducted using a general finite volume method, using the OpenFOAM CFD code. A dynamic mesh is used together with a sliding GGI interface to include the effect of the rotating runner. The hub and tip clearances are included in the runner. An analysis is conducted of the unsteady behavior of the flow field, the pressure fluctuation in the draft tube, and the coherent structures of the flow. The tangential and axial velocity distributions at three sections in the draft tube are compared against LDV measurements. The numerical result is in reasonable agreement with the experimental data, and the important flow physics close to the hub in the draft tube is captured. The hub and tip vortices and an on-axis forced vortex are realistically captured. The numerical results show that the frequency of the forced vortex in 1/5 of the runner rotation

A comparative study of scale-adaptive and large-eddy simulations of highly swirling turbulent flow through an abrupt expansion

The strongly swirling turbulent flow through an abrupt expansion is investigated using highly resolved LES and SAS, to shed more light on the stagnation region and the helical vortex breakdown. The vortex breakdown in an abrupt expansion resembles the so-called vortex rope occurring in hydro power draft tubes. It is known that the large-scale helical vortex structures can be captured by regular RANS turbulence models. However, the spurious suppression of the small-scale structures should be avoided using less diffusive methods. The present work compares LES and SAS results with the experimental measurement of Dellenback et al. (1988). The computations are conducted using a general non-orthogonal finite-volume method with a fully collocated storage available in the OpenFOAM-2.1.x CFD code. The dynamics of the flow is studied at two Reynolds numbers, Re=6.0×104 and Re=105 , at the almost constant high swirl numbers of Sr=1.16 and Sr=1.23, respectively. The time-averaged velocity and pressure fields and the root mean square of the velocity fluctuations, are captured and investigated qualitatively. The flow with the lower Reynolds number gives a much weaker outburst although the frequency of the structures seems to be constant for the plateau swirl number

Velocity and pressure fluctuations induced by the precessing helical vortex in a conical diffuser

The flow unsteadiness generated in the draft tube cone of hydraulic turbines affects the turbine operation. Therefore, several swirling flow configurations are investigated using a swirling apparatus in order to explore the unsteady phenomena. The swirl apparatus has two parts: the swirl generator and the test section. The swirl generator includes two blade rows being designed such that the exit velocity profile resembles that of a turbine with fixed pitch. The test section includes a divergent part similar to the draft tube cone of a Francis turbine. A new control method based on a magneto rheological brake is used in order to produce several swirling flow configurations. As a result, the investigations are performed for six operating regimes in order to quantify the flow from part load operation, corresponding to runaway speed, to overload operation, corresponding to minimum speed, at constant guide vane opening. The part load operation corresponds to 0.7 times the best efficiency discharge, while the overload operation corresponds to 1.54 times the best efficiency discharge. LDV measurements are performed along three survey axes in the test section. The first survey axis is located just downstream the runner in order to check the velocity field at the swirl generator exit, while the next two survey axes are located at the inlet and at the outlet of the draft tube cone. Two velocity components are simultaneously measured on each survey axis. The measured unsteady velocity components are used to validate the results of unsteady numerical simulations, conducted using the OpenFOAM CFD code. The computational domain covers the entire swirling apparatus, including strouts, guide vanes, runner, and the conical diffuser. A dynamic mesh is used together with sliding GGI interfaces to include the effect of the rotating runner. The Reynolds averaged Navier–Stokes equations coupled with the RNG k–ε turbulence model are utilized to simulate the unsteady turbulent flow throughout the swirl generator

Numerical Predictions of Slot Synthetic Jets in Quiescent Surroundings,

A detailed numerical simulation is undertaken to investigate physical processes that are engendered in the injection of synthetic (zero-net-mass-flux) jets into quiescent surroundings. A complementary study of 3-D unsteady Reynolds-averaged Navier-Stokes (URANS) applied to a nominally 2-D problem is carried out and compared with experimental data that are obtained at corresponding conditions with the aim of achieving an improved understanding of fluid dynamics of synthetic jets flow fields in the quiescent surroundings. Making this investigation allows the computational framework to be verified, and so the basic properties of synthetic jets to be comprehended. Of particular interest is acquiring the turbulent structures from undigested experimental data. The hierarchy of established coherent structures presented here provides a credible explanation for the turbulent characteristics that are observed both in the experiments and the simulations. The computations are conducted by OpenFOAM C++ with two turbulence models, SST and RSM, are used to predict the synthetic jets flow fields. Although the models are capable of simulating time-averaged turbulent quantities, they underestimate phase-averaged turbulent quantities. As Reynolds number increases, the underestimates intensify

Turbulence-resolving Simulations of Swirling Flows

A series of numerical investigations is undertaken using a wide range of turbulence mod-els including conventional and non-conventional URANS models, hybrid URANS-LESmethods and LES to capture a large variety of physical mechanisms that produce pres-sure pulsations in the swirling flows. The available knowledge about these pulsations,which are usual in hydropower, are still far from complete. When the swirl is moder-ately low, a stable on-axis structure generates in the pipe. If the swirl exceeds a certainlevel, the flow patterns associated with the swirl dominated vortex motions vacillate. Akey feature of strongly swirling flows is vortex breakdown. The vortex breakdown is anabrupt change in the core of a slender vortex and typically develops downstream into arecirculatory “bubble” or a helical pattern. The swirl effects are usually seen as either thedesired result of design or unavoidable, possibly unforeseen, side effects which comprise aforced vortex core centered around its axis of rotation. The vortex breakdown is an invis-cid process and the pulsations caused by the vortex breakdown and their impact on theefficiency and hydraulic structures of water turbines depend on the flow rate, the velocitydistribution after the runner, the shape of the draft tube, and the dynamic response ofthe whole hydraulic structure. The high level of unsteadiness in the flow field necessitatesthe utilization of appropriate turbulence treatments to predict the complexity of the flowstructures.Time-accurate Reynolds-averaged Navier-Stokes (URANS) models are primarily use-ful for capturing large-scale flow structures, while the details of the small-scale turbu-lence eddies are filtered out in the averaging process. In many cases also the large-scalestructures are damped by the URANS modeling which is formulated to model all theturbulence. The swirling flows in a pipe are dominated by large-scale detached eddies,therefore the URANS models should be capable of predicting the flow fields. The qual-ity of the URANS results is very dependent on the underlying turbulence model. Theknowledge about URANS is limited to the simplest (most robust) linear eddy-viscositymodels which are available in the proprietary codes. The inability of the conventionallinear eddy-viscosity models available in a CFD code should thus not be generalizedto the URANS method alone. The conventional linear eddy-viscosity model provides adirect link between the turbulent stress tensor and the mean strain rate, forcing themto be directly in phase, which is wrong. In the highly swirling flows, the curvature ofthe streamlines should be taken into account for a better predicting of the flow fields.Reynolds Stress Models (RSM) have the potential to significantly improve the flow pre-dictions by resolving anisotropy and incorporating more sensitivity and receptivity ofthe underlying instabilities and unsteadiness. Since they are difficult to use they arenot widely used in industry. Most of the RSMs are not robust for highly swirling flowsbecause of instability in the rapid part of the pressure-strain term in the transport equa-tion. The Explicit Algebraic Reynolds Stress Models (EARSMs) are simplified RSMsthat are much more numerically and computationally robust and have been found tobe comparable to standard two-equation models in computational effort. The EARSMsassume that the Reynolds stress tensor can be expressed in the strain and vorticity ratetensors.A more advanced approach, also called the second generation URANS method, is thehybrid URANS-LES method which is capable of capturing the high level of unsteadinessand handling the anisotropic and highly dynamic character of turbulent swirling flows.An extended series of turbulence models is scrutinized in this work while the main focusis on the Detached-eddy simulation (DES) method. The DES method is a promising hy-brid URANS-LES strategy capable of simulating internal flows dominated by large-scaledetached eddies at practical Reynolds numbers. Another hybrid URANS-LES methodis scale-adaptive simulation (SAS). This method is based on detecting the unsteadinessaccording to the velocity gradients in the flow field. This method gives better resultsthan LES in a highly swirling flow in a pipe using a relatively coarse resolution

Turbulence-resolving Simulations of Swirling Flows

A series of numerical investigations is undertaken using a wide range of turbulence mod-els including conventional and non-conventional URANS models, hybrid URANS-LESmethods and LES to capture a large variety of physical mechanisms that produce pres-sure pulsations in the swirling flows. The available knowledge about these pulsations,which are usual in hydropower, are still far from complete. When the swirl is moder-ately low, a stable on-axis structure generates in the pipe. If the swirl exceeds a certainlevel, the flow patterns associated with the swirl dominated vortex motions vacillate. Akey feature of strongly swirling flows is vortex breakdown. The vortex breakdown is anabrupt change in the core of a slender vortex and typically develops downstream into arecirculatory “bubble” or a helical pattern. The swirl effects are usually seen as either thedesired result of design or unavoidable, possibly unforeseen, side effects which comprise aforced vortex core centered around its axis of rotation. The vortex breakdown is an invis-cid process and the pulsations caused by the vortex breakdown and their impact on theefficiency and hydraulic structures of water turbines depend on the flow rate, the velocitydistribution after the runner, the shape of the draft tube, and the dynamic response ofthe whole hydraulic structure. The high level of unsteadiness in the flow field necessitatesthe utilization of appropriate turbulence treatments to predict the complexity of the flowstructures.Time-accurate Reynolds-averaged Navier-Stokes (URANS) models are primarily use-ful for capturing large-scale flow structures, while the details of the small-scale turbu-lence eddies are filtered out in the averaging process. In many cases also the large-scalestructures are damped by the URANS modeling which is formulated to model all theturbulence. The swirling flows in a pipe are dominated by large-scale detached eddies,therefore the URANS models should be capable of predicting the flow fields. The qual-ity of the URANS results is very dependent on the underlying turbulence model. Theknowledge about URANS is limited to the simplest (most robust) linear eddy-viscositymodels which are available in the proprietary codes. The inability of the conventionallinear eddy-viscosity models available in a CFD code should thus not be generalizedto the URANS method alone. The conventional linear eddy-viscosity model provides adirect link between the turbulent stress tensor and the mean strain rate, forcing themto be directly in phase, which is wrong. In the highly swirling flows, the curvature ofthe streamlines should be taken into account for a better predicting of the flow fields.Reynolds Stress Models (RSM) have the potential to significantly improve the flow pre-dictions by resolving anisotropy and incorporating more sensitivity and receptivity ofthe underlying instabilities and unsteadiness. Since they are difficult to use they arenot widely used in industry. Most of the RSMs are not robust for highly swirling flowsbecause of instability in the rapid part of the pressure-strain term in the transport equa-tion. The Explicit Algebraic Reynolds Stress Models (EARSMs) are simplified RSMsthat are much more numerically and computationally robust and have been found tobe comparable to standard two-equation models in computational effort. The EARSMsassume that the Reynolds stress tensor can be expressed in the strain and vorticity ratetensors.A more advanced approach, also called the second generation URANS method, is thehybrid URANS-LES method which is capable of capturing the high level of unsteadinessand handling the anisotropic and highly dynamic character of turbulent swirling flows.An extended series of turbulence models is scrutinized in this work while the main focusis on the Detached-eddy simulation (DES) method. The DES method is a promising hy-brid URANS-LES strategy capable of simulating internal flows dominated by large-scaledetached eddies at practical Reynolds numbers. Another hybrid URANS-LES methodis scale-adaptive simulation (SAS). This method is based on detecting the unsteadinessaccording to the velocity gradients in the flow field. This method gives better resultsthan LES in a highly swirling flow in a pipe using a relatively coarse resolution

Turbulence modelling of an unsteady periodic zero-net-mass flux jet

The purpose of this article is to present the results of a series of numerical simulations of zero-net-mass-flux (synthetic) jet actuators that are acquired by three turbulence models. Shear stress transport k–ω-based models, Reynolds stress ε-based models, and Reynolds stress ω-based models are applied and the results are compared along with the experimental data. Computations are performed with usual Reynolds-averaged Navier–Stokes equations solved in a time-dependent mode, for the simulation of a synthetic jet in quiescent environment. The collocated finite-volume approach is used by FOAM C++ library. The present investigation focuses on the ability of the turbulence models to substantiate the phase-averaged Reynolds equations. The reason of the poor reflection of phase-averaged values by numerical modelling is the crux of the current contribution but time-averaged values are predicted to be more reasonable