Turbulence Closure Model Research Articles

Numerical Analysis of Turbulent Flow over a Backward-facing Step in an Open Channel

Abstract Computational examinations of the flow field in an open channel having a single Backward--Facing Step (BFS) with a constant water depth of 1.5 m were performed. The e ects of the expansion ratio, and the flow velocity along the reattachment length, were investigated by employing two di erent expansion ratios of 1.5 and 2, and eight various flow velocities of 0.5, 1, 2, 3, 4, 5, 7.5 and 10 m/sec in the Computational Fluid Dynamic (CFD) simulations. Commercially available CFD software, ANSYS FLUENT, was used for calculations. The simulation outcomes were verified using experimental results. Moreover, analyses were performed by using two equation turbulence closure models, K-ɛ family (standard, RNG and realizable), and K-ω family (Wilcox’s and SST K-ω). The analyses have revealed that the reattachment length increases with an increase in the expansion ratio, the flow velocity and the Reynolds number. The results obtained for two expansion rates and eight di erent flow velocities have shown insignificant di erences between one turbulence closure model and the others. Furthermore, it was observed that both velocity and expansion ratios have an e ect on the reattachment zone size.

Statistical Analysis on The Near-Wake Region of RANS Turbulence Closure Models for Vertical Axis Tidal Turbine

The flow field in the near wake region (up to six turbine diameters downstream) of a tidal current turbine is strongly driven by the combined wake of the device support structure and the rotor. Accurate characterisation of the near-wake region is important, but it is dominated by highly turbulent, slow-moving fluid. At present, limited number of research has been undertaken into the characterisation of the near-wake region for a Vertical Axis Tidal Turbine (VATT) device using the Reynolds Averaged Navier Stokes (RANS) model in the shallow water environment of Malaysia. This paper presents a comprehensive statistical analysis using the Mean Absolute Error (MEA), Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) on the near-wake region for shallow water application by comparing numerical solutions (i.e., different types of RANS turbulence models using Ansys Fluent) with published experimental data. Seven RANS turbulence models with a single VATT, represented by using a cylindrical object, were employed in the preliminary study. The statistical analysis performed in this study is essential in exploring and giving a detailed understanding on the most suitable RANS turbulence model to be improved, specifically on its near-wake region. In this study, the near wake region is defined as D ≤ 6, where D is the device diameter. The analysis shows that the RANS numerical solutions are unable to accurately replicate the near-wake region based on large statistical errors computed. The average RMSE of near-wake region at z/D = [2, 3, 4, 6] are 0.5864, 0.4127, 0.4344 and 0.3577 while the average RMSE at far-wake region z/D = [8, 12] are 0.2269 and 0.1590, where z is the distance from the cylindrical object along the length of domain. The statistical error values are found to decrease with increasing downstream distance from a cylindrical object. Notably, the standard k–ε and realizable k–ε models are the two best turbulent models representing the near-wake region in RANS modelling, yielding the lowest statistical errors (RMSE at z/D = [2, 3, 4, 6] are 0.5666, 0.4020, 0.4113 and 0.3455) among the tested parameters

On the turbulence modelling of waves breaking on a vertical pile

Incipient wave breaking on a vertical circular pile is simulated with a Reynolds stress– $\omega$ turbulence model. Comparison of results simulated with a stabilized two-equation turbulence model, as well as no turbulence model, demonstrates that the breaking point and the peak force on a vertical cylinder due to incipient breaking should not be affected by the turbulence closure model, provided that it is stable and the simulations are converged. Notably, the present results show that the build-up to peak force induced by incipient wave breaking can be accurately predicted without any turbulence closure model. However, for the prediction of the secondary load cycle (SLC), proper turbulence modelling is required, as this process involves both turbulence production and lee-side flow separation. The Reynolds stress– $\omega$ model is demonstrated to predict the SLC more accurately than a stabilized two-equation $k$ – $\omega$ turbulence model, as the flow separation points and vorticity field are better predicted. Some existing studies indicate that the generation of the SLC does not necessarily result from flow separation, but is rather due to the suction force. The present work finds that the occurrence and point of flow separation significantly affect the magnitude of the suction force, which hence affects the SLC prediction significantly. For waves breaking on a vertical pile, proper turbulence modelling is therefore essential for accurate SLC predictions. (In the above, $k$ is the turbulent kinetic energy density and $\omega$ is the specific dissipation rate.)

An ISPH with modified k–ε closure for simulating breaking periodic waves

The Incompressible Smoothed Particle Hydrodynamics (ISPH) method, solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the modified k–ε turbulence closure developed by Wang and Liu (2020) [ Coastal Engineering , 157, 1–28], is further extended to periodic waves. The capability of this numerical model is demonstrated by applying it to three laboratory experiments: (1) Dynamics of surf-zone turbulence generated by a spilling breaker and a plunging breaker over a plane slope in small-scale wave flume experiments, (2) breaking wave generated turbulence over a stationary barred beach in large-scale wave flume experiments, and (3) spatial and temporal distributions of turbulence generated by bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. In this new ISPH model, the gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. The experimental data for the spilling breaker on a plane beach is used to calibrate the model. Once the model is calibrated, all the empirical coefficients in the turbulence closure model, including the stress limiter coefficient λ 3 , which is required in modifying the eddy viscosity, are fixed for the validation processes with other experimental data sets. All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. The differences between experimental observations and numerical simulations are quantified by the percentage error. Overall, good agreement is observed for all experiments. This paper presents the first comprehensively validated 2D ISPH model with the modified k–ε turbulence closure, which can be applied to periodic wave breaking problems. • The Incompressible Smoothed Particle Hydrodynamics (ISPH) method is coupled with the modified k–ε turbulence closure equations to solve the 2D RANS (Reynolds Averaged Navier-Stokes) equations. The gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. • The model has been checked with three laboratory experiments for periodic breaking waves. (1) Spilling and plunging cnoidal waves over a plane slope in small-scale wave flume experiments, (2) plunging periodic breaking wave over a stationary barred beach in large-scale wave flume experiments, and (3) bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. • All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. • The differences between experimental observations and numerical simulations are quantified by the percentage error. • Overall, good agreement is observed for all experiments. Good agreements are observed in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress.

Finite Element Numerical Simulation of Local Scour of a Three-Dimensional Cylinder under Steady Flow

Pile safety has received increasing attention in marine engineering, especially in the field of local scour. In this paper, a finite element numerical model is established for local scour around a cylinder in steady currents. The flow is described by unsteady Reynolds–averaged Navier–Stokes equations with a traditional turbulent closure model. The proposed scour model takes bed load into account. The Exner equation is solved to determine the bed variation and the moving mesh approach is used to capture the evolution of the bed. When the resulting slope exceeds the angle of repose, a novel sand-slide model based on Rodrigues' rotation formula is used to prevent simulation distortion. All the equations are discretized by the two-step Taylor–Galerkin algorithm, and the resulting approach is fast to implement with second-order accuracy in space. The numerical results are found to be in good agreement with the experimental data.

Frame invariant neural network closures for Kraichnan turbulence

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we put forth a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work opens up a possibility of connecting physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

Sensitivity analysis of a three-dimensional simulation of turbidity currents in a sloping flume

Sensitivity analysis is necessary in numerical models to establish the optimal model configuration and simulate turbidity currents accurately. The sensitivity of turbidity currents simulated by a three-dimensional numerical model named the semi-implicit cross-scale hydroscience integrated system model (SCHISM) was assessed using domain discretization, the turbulence closure model, and the transport scheme. The results show that a higher horizontal resolution with an appropriate aspect ratio, localized sigma coordinates with shaved cells (LSC2) grid with sufficient layers, a two-phase mixture turbulence closure model, and transport schemes with critical depth ratio lower than 1 could improve the model performance on the turbidity currents. The study can provide helpful guidance to establish accurate turbidity current simulations in complex water environments.

Physical Reasoning of Double- to Single-Loop Transition in Industrial Reactors using Computational Fluid Dynamics

Double- to single-loop pattern transition and a significant reduction in the power number with a decrease in the clearance of the Rushton turbine impeller in a baffled reactor was elucidated in earlier research works. The present work investigates the physical reasons behind these phenomena using the computational fluid dynamics approach. The Reynolds Averaged Navier–Stokes equations with standard turbulence model closure were used to model the turbulent flow conditions in the reactor vessels. The Multiple Reference Frame (MRF) approach was adopted to model the impeller baffle interactions in the reactor vessels. The implicit Volume of Fluid (VOF) method was employed to simulate the aeration process in the reactor configurations considered. The development of a low pressure region below the impeller of a low clearance vessel deflects the discharge streams downward, leading to the formation of a single-loop pattern. The downward movement of the discharge streams reduces the vortex activity behind the impeller blades, leading to weaker form drag and a decrease in the power number of the impeller. Similarly, a high clearance vessel provides a low pressure region above the impeller which deflects the discharge streams above the impeller, resulting in a single-loop pattern and a considerable increase in the air entrainment due to superior vortex and turbulence activity present near the free liquid surface. The standard reactor vessel was found to provide superior bulk mixing of fluid as the overall turbulent dissipation rate is 35% more than that associated with low and high clearance vessels.

Numerical proof of shell model turbulence closure

The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure, based on deep recurrent neural networks, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, we employ shell models of turbulence. Our results encourage the development of similar approaches for 3D Navier-Stokes turbulence.

On applicability of von Karman’s momentum theory in predicting the water entry load of V-shaped structures with varying initial velocity

The water landing of an amphibious aircraft is a complicated problem that can lead to uncomfortable riding situation and structural damage due to large vertical accelerations and the consequent dynamic responses. The problem herein is investigated by solving unsteady incompressible Reynolds-averaged Navier–Stokes equations with a standard k−ω turbulence closure model. The theoretical solutions established by the von Karman’s momentum theory are also employed. In order to validate the relationships between the initial vertical velocity and the peak value of vertical acceleration, free fall test cases of 2D symmetric wedge oblique entry and 3D cabin section vertical entry are presented first. The other parameters at which the maximum acceleration occurs, such as time, penetration depth, velocity, are also evaluated. Hence, the quantitative relations are investigated to water landing event for amphibious aircraft. Detailed results in terms of free surface shape and pressure distribution are provided to show the slamming effects. The results show that a linear dependence of the maximal acceleration from the square of initial vertical velocity can be derived for two-dimensional wedge, three-dimensional cabin section and seaplane with V-shaped hull. Moreover, the ratio between the corresponding velocity and the initial vertical velocity tends to a constant threshold value, 5/6, derived from the theoretical solution, when increasing the initial vertical velocity in all three cases.

Three-dimensional numerical simulations for mitigation of tsunami wave impact using intermittent sea dikes

Sea dikes are nowadays adopted for the protection of onshore infrastructures against devastating tsunami wave. For intermittent/discontinuous sea dikes, the flow fields are 3D in nature, making it necessary for three-dimensional model studies to analyze their effects on the peak tsunami impact force on a downstream structure. In this study, a numerical code based on a suitable turbulence closure model has been used to make simulations for trapezoidal sea dikes. The simulations have been performed for laboratory scale model. The simulation results for different dike length to gap ratios have shown that sea dikes with 25% gaps will be adequate as the peak impact force on an onshore building is reduced by 36%, while a continuous sea dike can reduce the peak impact force approximately by 40%. A composite dike wherein a 50% length of the larger trapezoidal cross-section is alternated with a smaller rectangular section is capable of reducing peak tsunami impact force by approximately 32%. Two staggered rows of intermittent dikes give better protection than a single row of intermittent dike. However, the protection is marginally lesser than that given by a single continuous dike.

Effect of fillets on a blade/vane of wave energy harvesting impulse turbine

Fillets on leading edges (LE) of turbine blades alter flow patterns and change the loss profile. A bidirectional flow impulse turbine utilized for harnessing wave energy is introduced and computational fluid dynamics (CFD) was used to perform various analysis. In the present work, fillets of different radii on the leading and trailing edges of both the rotor blade (RB) and guide vane (GV) are modified to study the change in overall performance. After an appropriate gird convergence study, ANSYS-CFX 16.0 solver is used for solving the Reynolds averaged Navier-Stokes (RANS) equations incorporating the k-ω-SST turbulence closure model. The numerical investigations were performed using the high-resolution scheme with the convergence criteria of 10−6 to produce unwavering results. The results show that the boundary layer near the endwall creates flow blockage and losses. Also, the increase in pressure drop due to the thickening of the boundary layers (BLs) across the blade/vane leads to a depletion in the overall performance of the turbine. The rotor and guide vane filleted turbine experience higher losses than the base model due to the radial pressure gradient that is explained with post-processed figures. The concept of fillet shapes has been applied to gas turbines and which improves the performance of the turbine due to a reduction in the secondary flow losses occurring inside the turbine and the same concept has been applied to wave energy air turbine to check its performance based on the losses present across the turbine passage.

On the Generalizability of Machine-Learning-Assisted Anisotropy Mappings for Predictive Turbulence Modelling

Several machine learning frameworks for augmenting turbulence closure models have been recently proposed. However, the generalizability of an augmented turbulence model remains an open question. We investigate this question by systematically varying the training and test sets of several models. An optimal three-term tensor basis expansion is used to develop a model-agnostic data-driven turbulence closure approximation. Then, hyperparameter optimization is performed for a random forest, a neural network, and an eXtreme Gradient Boosting (XGBoost) model. We recommend XGBoost for data-driven turbulence closure modelling owing to its low-tuning cost and good performance. We also find that machine learning models generalize well to new parametric variations of flows seen in the training dataset, but lack generalizability to new flow types. This generalizability gap suggests that machine learning methods are most suited for developing specialized models for a given flow type, a problem often encountered in industrial applications.

The Role of Turbulence in Fueling the Subsurface Chlorophyll Maximum in Tidally Dominated Shelf Seas

AbstractGlider observations show a subsurface chlorophyll maximum (SCM) at the base of the seasonal pycnocline in the North Sea during stable summer conditions. A colocated peak in the dissipation rate of turbulent kinetic energy suggests the presence of active turbulence that potentially generates a nutrient flux to fuel the SCM. A one‐dimensional turbulence closure model is used to investigate the dynamics behind this local maximum in turbulent dissipation at the base of the pycnocline (PCB) as well as its associated nutrient fluxes. Based on a number of increasingly idealized forcing setups of the model, we are able to draw the following conclusions: (a) only turbulence generated inside the stratified PCB is able to entrain a tracer (e.g., nutrients) from the bottom mixed layer into the SCM region; (b) surface wind forcing only plays a secondary role during stable summer conditions; (c) interfacial shear from the tide accounts for the majority of turbulence production at the PCB; (d) in stable summer conditions, the strength of the turbulent diapycnal fluxes at the PCB is set by the strength of the anticyclonic component of the tidal currents.

Assessment of turbulent heat flux models for URANS simulations of turbulent buoyant flows in ROCOM tests

Turbulent mixing in buoyant flows is an essential mechanism involved in many scenarios related to nuclear safety in nuclear power plants. Comprehensive understanding and accurate predictions of turbulent buoyant flows in the reactor are of crucial importance, due to the function of mitigating the potential detrimental consequences during postulated accidents. The present study uses URANS methodology to investigate the buoyancy-influenced flows in the reactor pressure vessel under the main steam line break accident scenarios. With a particular focus on the influence of turbulent heat flux closure models, various combinations of two turbulence models and three turbulent heat flux models are utilized for the numerical simulations of three ROCOM tests which have different characteristic features in terms of the flow rate and fluid density difference between loops. The simulation results are compared with experimental measurements of the so-called mixing scalar in the downcomer and at the core inlet. The study shows that the anisotropic turbulent heat flux models are able to improve the accuracy of the predictions under conditions of strong buoyancy whilst in the weak buoyancy case, a major role is played by the selected turbulence models with essentially a negligible influence of the turbulent heat flux closure models.

Numerical Simulation of Irregular Breaking Waves Using a Coupled Artificial Compressibility Method

Wave breaking is widely recognized as a very challenging phenomenon to emulate using numerical/computational methods. On that condition, the transition from modelling regular to irregular breaking waves is not trivial. Even though some issues are surpassed in CFD simulations, there still are two substantial problems to account for. The first one entails the proper generation of irregular waves in a numerical wave tank, while the second is the introduction of the turbulent regime of breaking in the solver. The present work addresses these two problems by employing the Stabilized k−ω SST model for turbulence closure and by proposing an efficient and accurate method for irregular wave generation. Apart from that, an artificial compressibility method is used for coupling the system of equations, which solves these equations in a non-segregated manner and overcomes problems pertaining to the existence of the interface in free-surface flows. The methodology is validated through the test case of irregular wave propagation over a submerged breaker bar and a piecewise sloped bottom, indicating the ability of the method to capture irregular breaking wave phenomena. Simulations are in fair agreement with experimental data regarding energy spectra and free surface time-series, while results suggest that the known over-prediction of turbulent kinetic energy (TKE) is significantly constrained by the stabilized k−ω SST model.

Numerical Modeling of Horizontal Axis Wind Turbine: Aerodynamic Performances Improvement Using an Efficient Passive Flow Control System

In this paper, we explore the improvement of the aerodynamic characteristics of wind turbine blades under stall conditions using passive flow control with slots. The National Renewable Energy Laboratory (NREL) Phase II rotor, for which detailed simulations and experimental data are available, served as a baseline for assessing the flow control system effects. The position and configuration of the slot used as a flow control system were determined using CFD analysis. The 3D-RANS equations are solved with ANSYS FLUENT using the k-ω SST turbulence closure model. The pressure coefficient for different wind speeds for the baseline configuration is compared to the available experimental data. The comparison shows that CFD results were better for the attached flow. The current work consists of a 3-D CFD modeling of a rotating blade equipped with different flow control systems: single-slot (S-S) and two-slots (T-S). The computation provides a better understanding of the influence of these flow control devices on the performance of wind turbine blades, the control of boundary layer separation, and the rotation effect. These control systems increase the power output by over 60% at high wind speeds with large separated boundary layer regions. For the configuration with the control system, the slot has shown its ability to delay the boundary layer separation. However, the improved aerodynamic performance has been proven for medium and high angles of attack where the flow is generally in the stall condition. The addition of the second slot changed the flow behavior, and an improvement was observed compared to the single slot configuration. The results are helpful for the design and development of a new generation of wind turbine blades.

Uncertainty analysis of turbulence model in capturing flows involving laminarization and retransition

Flows experiencing laminarization and retransition are universal and crucial in many engineering applications. The objective of this study is to conduct an uncertainty quantification and sensitivity analysis of turbulence model closure coefficients in capturing laminarization and retransition for a rapidly contracting channel flow. Specifically, two commonly used turbulence models are considered: the Spalart-Allmaras (SA) one-equation model and the Menter Shear Stress Transport (SST) two-equation model. Thereby, a series of steady Reynolds Averaged Navier-Stokes (RANS) predictions of aero-engine intake acceleration scenarios are carried out with the purposely designed turbulence model closure coefficients. As a result, both SA and SST models fail to capture the retransition phenomenon though they achieve pretty good performance in laminarization. Using the non-intrusive polynomial chaos method, solution uncertainties in velocity, pressure, and surface friction are quantified and analyzed, which reveals that the SST model possesses much great uncertainty in the non-laminar regime, especially for the logarithmic law prediction. Besides, a sensitivity analysis is performed to identify the critical contributors to the solution uncertainty, and then the correlations between the closure coefficients and the deviations of the outputs of interest are obtained via the linear regression method. The results indicate that the diffusion-related constants are the dominant uncertainty contributors for both SA and SST models. Furthermore, the remarkably strong correlation between the critical closure coefficients and the outputs might be a good guide to recalibrate and even optimize the commonly used turbulence models.

Large-eddy simulations of gravity currents in the presence of waves

Simulations are performed to investigate gravity currents in the presence of free surface waves using the open-source computational fluid dynamics programme REEF3D with the concentration equation, and the large eddy simulation model for turbulence closure. Simulations show that the period of the oscillation front relates only to the period of the incident waves and the oscillation amplitude increases with wave height. The average velocity of the density current increases with increasing wave height and wavelength. The surface waves change the generation position and combination direction of the turbulence structures in the pycnocline. The oscillatory motion of the waves stabilizes the pycnocline earlier and reduces the turbulent mixing. The instability zone is reduced faster with higher wave heights with well-ordered K-H billows, but not for longer wavelengths. The instantaneous velocity and concentration fields are highly influenced by the incident wave characteristics when compared to that in the absence of waves.

CFD assessment of wind energy potential for generic high-rise buildings in close proximity: Impact of building arrangement and height

High-rise building complexes are of great importance for enabling sustainable urban development in large parts of the world. Earlier studies have indicated that high wind speed regions can be present along the passage between two high-rise buildings as well as above the roofs. At such locations, urban wind energy could be harvested by installing wind turbines between and/or above the roof of the buildings. However, the available wind energy potential around an array of generic high-rise buildings in close proximity has not yet been assessed for different building configurations. This paper conducts a detailed evaluation of the impacts of the building arrangement and height for a 2 × 2 array with a building height-to-street width ratio of 30 on the mean wind velocity and the wind energy potential along the passages between both upstream and downstream buildings as well as on their roofs. The following parameters are analyzed: (i) the passage width between the two upstream buildings (w), (ii) the streamwise distance between the upstream and downstream buildings (d), and (iii) the height difference between the upstream and downstream buildings (ΔH). The 3D steady Reynolds-averaged Navier-Stokes (RANS) equations are solved using the Reynolds stress model (RSM) turbulence model for closure. The CFD results are validated using wind-tunnel measurements of mean wind speed and turbulence intensity performed for the same building array. The results show elevated wind power density along the upstream passages for small w (=0.15B), high d (=0.6B), and equal building height (ΔH = 0). In contrast, comparatively high values of w, small d, and ΔH < 0 yield high wind power densities between the downstream buildings. Among the different wind turbine types considered, horizontally-mounted vertical axis wind turbines seem the most promising option for wind energy harvesting between the buildings.