Two-equation Turbulence Closure Research Articles

Nozzle Flow Separation Phenomena and Control for different conditions

A detailed study of separated nozzle flows has been conducted. For a subscale, non-axisymmetric, two-dimensional, convergent divergent nozzle, schlieren flow visualization was acquired along with measurements of force, moment, and pressure as part of an extensive static performance evaluation. Additionally, two-dimensional numerical simulations were performed using the computational fluid dynamics package PAB3D together with algebraic Reynold’s stress modelling and two-equation turbulence closure. This study's experimental findings show that shock-induced boundary layer separation, which was classified into two distinct flow regimes: three-dimensional separation with partial reattachment and entirely detached two-dimensional separation, dominated off design over expanded nozzle flow. The impact of variable shock generation and reflections in various nozzle types on the two primary separation modes, namely Free and Restricted Shock Separation (FSS & RSS), is investigated. The flow separation problem in rocket nozzles has been an unwelcome phenomenon for engineers ever since the birth of the space era. Naturally, the engineers were given the job of bringing things under control. But it proved to be a difficult endeavor; despite the fact that many people were able to explain the physics underlying this occurrence, it is still not completely understood today.

RANS Modelling of a NACA4412 Wake Using Wind Tunnel Measurements

Wake analysis plays a significant role in wind-farm planning through the evaluation of losses and energy yield. Wind-tunnel tests for wake studies have high costs and are time-consuming. Therefore, computational fluid dynamics (CFD) emerges as an efficient alternative. An especially attractive approach is based on the solution of the Reynolds-averaged Navier–Stokes (RANS) equations with two-equation turbulence closure models. The validity of this approach and its inherent limitations, however, remain to be fully understood. To this end, detailed wind-tunnel experiments in the wake of a NACA4412 wing section profile are compared with CFD results. Two- and three-dimensional RANS simulations are carried out for a range of angles of attack up to stall conditions at a chord- and inflow-based Reynolds number of Rec=4×105. Here, we aim to investigate the wake characteristics and self-similar behaviour, both from the experimental and numerical perspectives. The measurements are carried out by means of hot-wire anemometry capturing the wake pattern in several planes. The sensitivity of the CFD model to different configurations of the setup and the considerations required for reliable simulation are discussed. The agreement between CFD, experiments, and the literature is fairly good in many aspects, including the self-similar behaviour and wake parameters, as well as the flow field. Comparison of experiments with URANS/RANS data indicates that the latter is an adequate methodology to characterize wings and their wakes once the CFD setup is designed appropriately and the limitations due to discretization and turbulence modelling are considered.

Radiused Edge Blade Tip for a Wider Operating Range in Wells Turbine

The narrow operating range of a Wells turbine restricts its energy extraction capability from the ocean waves. In this work, the concept of a radiused edge tip blade (RETB) was introduced to overcome such an issue. The RET modifies the tip and changes the tip leakage flow behaviour. The flow through the turbine annulus was simulated numerically and compared with the existing experimental results of the reference turbine. Three-dimensional Reynolds-averaged Navier–Stokes equations with a two-equation turbulence closure model available in ANSYS CFX 14.5 was used for the simulations. The computational domain was discretized with unstructured tetrahedral elements, and the grid independence study gave an optimal grid. The RETB altered the tip leakage flow characteristics and delayed the stall inception. The RETB enhanced the relative operating range by 25% and peak torque by 37%.

NEW METHODS FOR STABILIZING RANS TURBULENCE MODELS WITH APPLICATION TO LARGE SCALE BREAKING WAVES

Recently, Larsen and Fuhrman (2018) have shown that seemingly all commonly used (both k-omega and k-epsilon variants) two-equation RANS turbulence closure models are unconditionally unstable in the potential flow beneath surface waves, helping to explain the wide-spread over-production of turbulent kinetic energy in CFD simulations, relative to measurements. They devised and tested a new formally stabilized formulation of the widely used k-omega turbulence model, making use of a modified eddy viscosity. In the present work, three new formally-stable k-omega turbulence model formulations are derived and tested in CFD simulations involving the flow and dynamics beneath large-scale plunging breaking waves.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/T2fFRgq3I8E

Instability of the realizable k– ε turbulence model beneath surface waves

Recent research has proved that most widely used two-equation turbulence closure models are unconditionally unstable in regions of nearly potential flow having finite strain, as commonly found beneath non-breaking surface waves. In this work, we extend such analysis to consider the popular realizable k–ε turbulence model. It is proved that this model, unlike all others thus far analyzed, is only conditionally unstable in such regions due to the addition of viscosity in the ε dissipation term. A method for formally stabilizing the model in the problematic regions is likewise developed. The results of the analysis, using both standard and stabilized turbulence closures, are confirmed via numerical simulations of progressive surface wave trains using a computational fluid dynamics model. Important qualitative differences are likewise demonstrated in simulations involving spilling breaking waves. (In the above, k is the turbulent kinetic energy density, and ε is the turbulence dissipation rate.)

Stabilized RANS simulation of surf zone kinematics and boundary layer processes beneath large-scale plunging waves over a breaker bar

This paper presents numerical simulations of a bichromatic wave group propagating and breaking over a fixed breaker bar. The simulations are performed using a newly stabilized Reynolds-averaged Navier–Stokes (RANS) two-equation turbulence closure, which solves the longstanding problem of over-production of turbulence beneath surface waves in the nearly potential flow region prior to breaking. This model has previously been tested on small-scale spilling breaking regular waves, whereas in this work focus is on full (rather than model) scale application, wave groups (rather than regular waves) and plunging (rather than spilling) breakers. Additionally this paper has novel emphasis on bottom boundary layer dynamics which are very important for cross-shore sediment transport predictions. The model is validated by comparing with results from a previous experimental campaign. The model is shown to predict the surface elevations, velocities and turbulence well in the shoaling and outer surf-zone, avoiding turbulence over-production and incorrect undertow structure typical of standard turbulence closures. Comparison with detailed boundary layer measurements in the shoaling position reveals that the model is able to accurately capture the temporal dynamics of the entire wave boundary layer, including evolution of the boundary layer thickness, velocity overshoot and phase-shifts. Comparison in the surf zone additionally reveals that the model is able to accurately capture the transport of breaking-induced turbulence into the wave boundary layer. The performance of the model indicates that it can be used directly in the simulation of cross-shore sediment transport and morphology and also be used to study important hydrodynamic processes, which can help improve the predictive skill of morphodynamic profile models applied in coastal engineering.

Discontinuous Galerkin discretization for two-equation turbulence closure model

Accurate representation of vertical turbulent fluxes is crucial for numerical ocean modeling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two dynamic equations to the system. Solving these equations numerically, however, is challenging due to the strict requirement of positivity of the turbulent quantities (e.g., turbulence kinetic energy and its dissipation rate), and the non-linear source terms that may render the numerical system unstable. In this paper, we present a Discontinuous Galerkin (DG) finite element discretization of the Generic Length Scale (GLS) equations designed to be incorporated in a DG coastal ocean model, Thetis. To ensure numerical stability, the function space for turbulent quantities must be chosen carefully. In this work, we propose to use zeroth degree elements for the turbulent quantities and linear discontinuous elements for the tracers and velocity. The spatial discretization is completed with a positivity preserving semi-implicit time integration scheme. We validate the implementation with standard turbulence closure model benchmarks and an idealized estuary simulation. Finally, we use the full three-dimensional model to simulate the Columbia River plume. The results confirm that the coupled model generates realistic vertical mixing, and remains stable under strongly stratified conditions and strong tidal forcing. River plume characteristics are well captured.

Numerical Simulation of Turbulent Flow and Pollutant Dispersion in Urban Street Canyons

In this study, we have developed a numerical model based on an open source Computational Fluid Dynamics (CFD) package OpenFOAM, in order to investigate the flow pattern and pollutant dispersion in urban street canyons with different geometry configurations. In the new model, the pollutant transport driven by airflow is modeled by the scalar transport equation coupling with the momentum equations for airflow, which are deduced from the Reynolds Averaged Navier-Stokes (RANS) equations. The turbulent flow calculation has been calibrated by various two-equation turbulence closure models to select a practical and efficient turbulence model to reasonably capture the flow pattern. Particularly, an appropriate value of the turbulent Schmidt number has been selected for the pollutant dispersion in urban street canyons, based upon previous studies and careful calibrations against experimental measurements. Eventually, the numerical model has been validated against different well-known laboratory experiments in regard to various aspect ratios (a relationship between the building height and the width of the street canyon), and different building roof shapes (flat, shed, gable and round). The comparisons between the numerical simulations and experimental measurements show a good agreement on the flow pattern and pollutant distribution. This indicates the ability of the new numerical model, which can be applied to investigate the wind flow and pollutant dispersion in urban street canyons.

Numerical investigation into the effect of burner swirl direction on furnace and superheater heat absorption for a 620 MWe opposing wall-fired pulverized coal boiler

The paper investigates the effects of pulverized coal swirl burners’ secondary air swirl directions on furnace water-wall, platen superheater and high temperature superheater heat absorption by using numerical simulations. The resultant effect on the carbon-monoxide and unburnt carbon levels was also investigated to establish the furnace performance. The conventional RANS approach was used along with a two-equation turbulence closure model to simulate the multispecies gas phase flow. Fuel particles were modeled as a discrete phase. The gas phase combustion was simulated using the eddy dissipation finite rate kinetics model and the surface reactions using a diffusion-kinetics limited model. To establish the validity of the modelling approach an actual 620 MWe boiler furnace and its superheaters were modelled, and the results compared to processed plant data. Once the model showed that it can predict the plant performance with reasonable accuracy it was used to investigate the performance changes for various burner swirl arrangements. Six swirl arrangement cases were simulated to determine the effect on the furnace performance indicators. It was found that by swirling all the burners per wall in the same direction that the furnace heat absorption could be increased by up to 6.67% and the unburned carbon fraction reduced from 0.029% to 0.022% when compared to the current boiler swirl configuration results, which has a staggered swirl direction arrangement. Furthermore, it was shown that the enhanced mixing in the volume adjacent to the burners also reduced the carbon-monoxide levels. The simulations demonstrated, for the given modelling methodology, that there is indeed interaction between adjacent burners which influences the combustion rate and in turn heat absorption in the water-cooled furnace walls and platen superheater for the modelled boiler.

High-performance ocean energy harvesting turbine design – Detailed flow analysis with blade leaning strategy

Oscillating water column wave energy converter is having low efficiency because of its principal component, a bidirectional turbine. An analysis of the internal flow of the turbine gives an idea of improving the performance through optimization of geometrical parameters. In this study, an impulse turbine of 0.3 m diameter with fixed guide vanes is numerically simulated by solving three-dimensional incompressible steady Reynolds averaged Navier-stokes equation with two-equation turbulence closure model. This study shows that the numerical results very well match with the experimental results. The detailed flow physics demonstrates that different types of losses occur in this type of turbine and shows that the downstream diverging path of the rotor and guide vane is responsible for low performance. In this study, the effect of guide vane lean, as well as the combined rotor and guide vane lean on the performance of the turbine, has been discussed in detail and found to increase the efficiency of the turbine.

On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

Performance Optimization of Centrifugal Pump for Crude Oil Delivery

Crude oil transport is an essential task in oil and gas industries, where centrifugal pumps are extensively used. The design of a centrifugal pump involves a number of independent parameters which affect the pump performance. Altering some of the parameters within a realistic range improves pump performance and saves a significant amount of energy. The present research investigated the pump characteristics by modifying the number of blades and the exit blade-angles. Reynolds-Averaged Navier-Stokes equations with standard k-ε two-equation turbulence closure were used for steady and incompressible flow of crude oil through the pump. The experimental set-up was installed and the pump performance calculated numerically was compared with the experiments. The investigations showed that the number of blades and the exit blade-angles have a significant influence on the head, shaft power, and efficiency. The vortical flow structures, recirculation and reverse flow characteristics around the impeller were investigated to explain the flow dynamics of impeller and casing. A larger number of blades on the rotor showed dominant streamlined flow without any wake phenomena. The combined effect of the number of blades and exit blade angle has led to an increase in head and efficiency through the parametric optimization.

Topology optimization of turbulent flows

The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient-based design process which minimizes an objective and satisfies a set of selected design constraints by distributing material in a design domain. The gradients are obtained using adjoint sensitivity analysis which requires solutions of a forward state problem and an additional adjoint problem. In the presented article the forward solver is based on finite volume discretized Reynolds-averaged Navier–Stokes equations coupled with either one- or two-equation turbulence closure models, and the adjoint solver is obtained via automatic differentiation. The presented approach is demonstrated on the optimization of several 2D and 3D examples including a detailed comparison to designs and sensitivities obtained with different turbulence models and under a frozen turbulence assumption. The results demonstrate the importance of exact sensitivity analysis and open new possibilities for the design of large scale multiphysics problems involving turbulent flows.

The nonlinear effects of the eddy viscosity and the bottom friction on the Lagrangian residual velocity in a narrow model bay

The nonlinear effects of the eddy viscosity and the bottom friction on the Lagrangian residual velocity (LRV) are studied numerically in a narrow model bay. Three groups of the experiments with different eddy viscosity and different forms of the bottom friction are designed and are carried out in the three kinds of the topography. When the eddy viscosity is obtained from a two-equation turbulence closure model, the pattern of the LRV is more complex than that of the time invariant eddy viscosity case and the intensity is from more than 1.3 times to one order smaller than that of the linear eddy viscosity condition. The LRV are also acquired when the eddy viscosity varies from the flood-averaged one to the ebb-averaged one. It is found that when the flood-averaged eddy viscosity is bigger than the ebb-averaged eddy viscosity (flood-dominated asymmetry), the direction of the breadth-averaged LRV and the 3D LRV is nearly opposite to that when the eddy viscosity asymmetry is reverse (ebb-dominated asymmetry). However, the intensity of the LRV for the ebb-dominated case decreases toward the flood-dominated case as the ratio of the maximum depth in the deep channel and the minimum depth on the shoal increases. The different forms of the bottom friction also play a role in the LRV. The structures of the 3D LRV and the depth-integrated LRV are simpler, and the intensity of the LRV is two times smaller when the linear bottom friction is used than those when the quadratic bottom friction is used.

Experimental Study and Simulation of a Small-Scale Horizontal-Axis Wind Turbine

The advancement of wind energy as an alternative source to hydrocarbons depends heavily on research activities in turbulence modeling and experimentation. The velocity deficit behind wind turbines affects the power output and efficiency of a wind farm. Being able to simulate the wake dynamics of a wind turbine effectively can result in optimum spacing, longer wind turbine life, and shorter payback on the wind farm investment. Two-equation turbulence closure models, such as k–ε and k–ω, are used extensively to predict wind turbine performance and velocity deficit profiles. The application of the Reynolds stress model (RSM) turbulence closure method has been limited to few studies where the rotor is modeled as an actuator disk (AD). The computational cost associated with RSM has made it challenging for simulations where the rotor is discretized directly; however, with advances in computer speed and power coupled with parallel computing architecture, RSM may be a better turbulence closure option. In this research, wind tunnel experiments were conducted, using hot-wire anemometry, to measure the velocity deficit profiles at different wake locations behind a small-scale, three-bladed, horizontal-axis wind turbine (HAWT). Experiments were also performed with two and three HAWTs in series to evaluate the change in velocity deficit and turbulence intensity (TI). High-speed imaging with an oil-based mist captured the vortices produced at the blade tips and showed the vortices dissipated approximately three rotor diameters downstream. Computational fluid dynamics (CFD) simulations were performed to predict the velocity deficit at wake locations matching the experiments. The Reynolds stress model was applied to a fully discretized rotor with a tower and nacelle included in the simulation. A steady-state moving reference frame (MRF) model was created with the computational domain subdivided into rotating and stationary domains. The MRF results were used as an initial condition for time-accurate rigid body motion (RBM) simulations. The RBM CFD simulations showed excellent agreement with experimental measurements for velocity deficit after properly accounting for experimental boundary effects. Isosurfaces of the Q-criterion highlighted the vortices produced at the blade tips and were consistent with high-speed images.

Adapted two-equation turbulence closures for actuator disk RANS simulations of wind & tidal turbine wakes

Reliable methods for modelling wake recovery within a farm of wind or tidal turbines are critical for obtaining accurate estimates of annual energy production, and for detailed farm layout optimization. These are important objectives for maximizing energy yield while minimizing costs. Computational fluid dynamics (CFD) simulation is rapidly being adopted as a tool for flow modelling in wind and tidal farms, gaining favour over more traditional and simpler empirically-determined wake models. The most practical methodology for CFD simulations of turbine farms uses an actuator disk (AD) representation for each rotor, which imposes the rotor forces by adding source terms to the governing equations rather than explicitly resolving the flow over the turbine blades. It is well understood that when using the AD approach, standard turbulence models tend to predict faster wake recovery than is observed in real flows. Thus, the standard CFD turbulence models must be adapted for use with the AD methodology. Additionally, because of the manner in which the AD approach distributes the rotor forces, it cannot resolve the system of discrete vortices trailed from the blade tips.This article presents two contributions to improving AD simulations of wind/tidal turbine wakes. The first is identifying that the well-established k-ω SST turbulence model is appropriate for AD simulations because it mitigates the problem of over-predicting the initial wake recovery rate. The second contribution is a method to include the typically un-modelled production of turbulent kinetic energy due to the breakdown of trailed vortices. This method was tuned to minimize the wake error for three experimental test cases with different rotors and different ambient turbulence intensities {3,10,15}%. The new model was validated and compared to existing turbulence methods for the wake of a second rotor in a tandem array configuration with different separation distances and ambient turbulence intensities. The different models were assessed using an error metric designed to estimate the error in predicting the power production of a turbine array. The reduction of this error by the new model varied from case to case, but was on the order of 3.5–10%, compared to the standard k-ε model.

On the modeling of wave-enhanced turbulence nearshore

A high resolution k–ω two-equation turbulence closure model, including surface wave forcing was employed to fully resolve turbulence dissipation rate profiles close to the ocean surface. Model results were compared with observations from Surface Wave Instrument Floats with Tracking (SWIFTs) in the nearshore region at New River Inlet, North Carolina USA, in June 2012. A sensitivity analysis for different physical parameters and wave and turbulence formulations was performed. The flux of turbulent kinetic energy (TKE) prescribed by wave dissipation from a numerical wave model was compared with the conventional prescription using the wind friction velocity. A surface roughness length of 0.6 times the significant wave height was proposed, and the flux of TKE was applied at a distance below the mean sea surface that is half of this roughness length. The wave enhanced layer had a total depth that is almost three times the significant wave height. In this layer the non-dimensionalized Terray scaling with power of −1.8 (instead of −2) was applicable.

Parameterizing suspended canopy effects in a three-dimensional hydrodynamic model

ABSTRACTThis paper presents an amendment of an existing three-dimensional hydro-environmental model (Environmental Fluid Dynamics Code) to incorporate effects of suspended canopies on the vertical flow structure. Five different modelling approaches are investigated, encompassing hydrodynamic form drag imparted by the suspended canopy, an amended two-equation turbulence scheme representing turbulence generated locally by elements within the canopy, and three separate formulations for vertical profiles of drag coefficients. Data from laboratory experiments with rigid cylinders are used to validate the calculations of velocity and shear stresses. The results show that the most accurate reproduction of the canopy flow was obtained using a vertically varying drag coefficient along with a two-equation turbulence closure scheme that includes additional turbulence production and dissipation terms. The numerical model reproduced velocity profiles accurately, but the shear stresses are slightly overestimated.

Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k˜−ε˜,k˜−w˜, and k˜−ω˜ , were used to close the non-simplified quasi-three dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k˜−ω˜ model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.

Combined tidal and wind driven flows and residual currents

The effect of a residual current on the combined tidal and wind driven flow and the resulting bedload sediment transport in the ocean has been investigated, using a simple one dimensional two-equation turbulence closure model. Predictions of the combined tidal and wind driven flow with given residual currents are presented, showing that the residual current has a substantial effect on both the depth averaged mass transport and the mean bedload transport directions; in some cases the effect of the residual current is to almost reverse the mean bedload transport direction. The residual current affects the rotation of the flow due to the Coriolis effect in the lower part of the water column (the near-surface flow is wind dominated), causing a larger or smaller clockwise rotation of the depth averaged mass transport, depending on the direction of the residual current.