Reynolds-averaged Navier-Stokes Model Research Articles

Wave and Roller Transformation Over Barred Bathymetry

AbstractThe cross‐shore transformation of breaking‐wave roller momentum and energy on observed barred surfzone bathymetry is investigated with a two‐phase Reynolds Averaged Navier Stokes model driven with measured incident waves. Modeled wave spectra, wave heights, and wave‐driven increases in the mean water level (setup) agree well with field observations along transects extending from 5‐m water depth to the shoreline. Consistent with prior results the roller forcing contributes 50%–60% to the setup, whereas the advective terms contribute ∼20%, with the contribution of bottom stress largest (up to 20%) for shallow sandbar crest depths. The model simulations suggest that an energy‐flux balance between wave dissipation, roller energy, and roller dissipation is accurate. However, as little as 70% of the modeled wave energy ultimately dissipated by breaking was first transferred from the wave to the roller. Furthermore, of the energy transferred to the roller, 15%–25% is dissipated by turbulence in the water column below the roller, with the majority of energy dissipated in the aerated region or near the roller‐surface interface. The contributions of turbulence to the momentum balance are sensitive to the parameterized turbulent anisotropy, which observations suggest increases with increasing turbulence intensity. Here, modeled turbulent kinetic energy dissipation decreases with increasing depth of the sandbar crest, possibly reflecting a change from plunging (on the steeper offshore slope of the bar) to spilling breakers (over the flatter bar crest and trough). Thus, using a variable roller front slope in the roller‐wave energy flux balance may account for these variations in breaker type.

CFD simulations of turbulent flow and dispersion in built environment: A perspective review

Computational fluid dynamics (CFD), a powerful analysis tool in wind engineering, has been applied to a wide variety of problems over the past few decades. The application of CFD to environmental wind problems in the built environment is much more common than its application to structural wind problems, in both practice and research. This paper briefly reviews the history of urban wind problems and the development of wind engineering. Then, the progress in the applications of CFD to environmental problems is outlined, particularly in terms of the evolution of the studies presented over time at the International Conferences on Wind Engineering. The major achievements of CFD in environmental wind engineering in the last 30 years are discussed in terms of Large Eddy Simulation versus the Reynolds-averaged Navier-Stokes model, appropriate boundary conditions, verification and validation, and best practice guidelines. Furthermore, notable topics in recent applications of CFD to the built environment, including complicated particle (e.g., snow, rain, sand, sea salt) dispersion, are reviewed. Finally, the future direction of the applications of CFD to environmental problems as an advanced design and research tool is discussed.

Characteristics of Laminar Separation Bubble with Varying Leading-Edge Shapes and Deflections of the Trailing-Edge Flap

Abstract A series of Implicit Large Eddy Simulations (ILES) is carried out to examine the characteristics of a leading edge (LE) separation bubble. The test case comprises a flat plate with an elliptic leading edge which is equipped with a trailing edge flap. Simulations are carried out (a) at three different flap angles (20, 30, 90 degrees) and (b) using two different geometries of Elliptic Leading Edge (ELE) where the ratio of the semi-major to semi-minor axis is set to either 2:1 or 4:1. The flap is modeled using the immersed boundary method which is computationally economical as it avoids regenerating the grid for varying flap angles. The results show that (a) the flow separates at lower flap angles with a decrease in the aspect ratio of the ELE from 4:1 to 2:1 (b) an increase in the flap angle promotes separation at the LE due to an increase in the blockage in the bottom passage and a subsequent increase in the flow incidence at the leading edge. Simulations are carried out using the Gamma-Retheta transition model and comparisons are drawn against ILES and experiments. Although the qualitative trends predicted using both ILES and Reynolds Averaged Navier-Stokes (RANS) agree with experiments, both approaches predict relatively shorter separation bubbles. This is attributed to the excess flow blockage in experiments due to the support plates which are not modeled in the simulations. Nevertheless, the results demonstrate the superior accuracy of ILES over the RANS model.

Validation of helicity-corrected Spalart-Allmaras model for corner separation prediction in incompressible flow with OpenFOAM

Steady Reynolds-averaged Navier-Stokes (RANS) computations save significant computational resources compared to unsteady RANS and large eddy simulation (LES). However, the ability of most RANS models to accurately predict flow separation in compressor/fan blade rows is limited. Recent research focused on reducing the computational cost of predicting compressor/fan stall points with steady computations has shown that the helicity-corrected Spalart-Allmaras (SA) turbulence model is able to avoid over-predicting corner separations and thus lead to converged RANS up to the actual stall point. To date, this model has mostly been implemented in in-house codes or in commercial codes as a user add-on, where the source code is not available. In a recent paper, the authors implemented the helicity-corrected SA model in OpenFOAM, an open-source CFD package. In this paper, the differences in the flow field for RANS solutions with the original SA model, the helicity-corrected SA model, and Menter’s shear stress transport (SST) model are highlighted for a linear cascade with incompressible flow. A NACA 65-1810 cascade is used, and computational results are compared to experimental data.

Turbulent Particle Flow in Spent Nuclear Fuel Storage Systems

Deposition models are being developed with the commercial computational fluid dynamics software STAR-CCM+ to evaluate particulate deposition on spent nuclear fuel (SNF) canisters. The primary particulate of concern is chloride salts, which are dispersed in the atmosphere and then deposited onto the canisters. During dry storage, the primary degradation process is likely to be chloride-induced stress corrosion cracking (CISCC) at the heat-affected zones of the canister welds. It is known that stainless steel canisters are susceptible to CISCC; however, the rate of chloride deposition onto the canisters is poorly known, based on sparse field data from a small number of sites. This paper describes work looking at various approaches to modeling turbulence, such as Reynolds-averaged Navier Stokes (RANS) and large eddy simulation (LES), and its impact on particle flow and deposition within a ventilated SNF storage system. The deposition rate is determined for a vertical canister system and a horizontal canister system. LES has the potential to simulate turbulent flows more accurately versus RANS, but is much more computationally expensive. A k-omega version of the RANS turbulence model was used for this study. The computational efficient RANS steady-state model predicted a similar canister deposition result as the LES simulation for a vertical canister storage system. For a horizontal storage system, the RANS steady-state model predicted more particles depositing on the canister than the LES simulation, providing a conservative estimation for particle deposition. A wall correction factor was added to the RANS model to dampen the turbulence fluctuation normal to a surface that left undamped, leads to the RANS model overpredicting deposition along a surface for smaller particles. This work was done to further development of deposition models that could be used to plan and inform SNF canister aging management programs with predictive models for the timing and occurrence of canister CISCC. This work is part of a larger effort tasked with understanding the likelihood of canister degradation due to CISCC. These models are still under development, and testing is needed for validation. However, these models are being presented now to demonstrate to canister vendors, utilities, regulators, and stakeholders the value of this type of modeling.

Deep Reinforcement Learning-Augmented Spalart–Allmaras Turbulence Model: Application to a Turbulent Round Jet Flow

The purpose of this work is to explore the potential of deep reinforcement learning (DRL) as a black-box optimizer for turbulence model identification. For this, we consider a Reynolds-averaged Navier–Stokes (RANS) closure model of a round turbulent jet flow at a Reynolds number of 10,000. For this purpose, we augment the widely utilized Spalart–Allmaras turbulence model by introducing a source term that is identified by DRL. The algorithm is trained to maximize the alignment of the augmented RANS model velocity fields and time-averaged large eddy simulation (LES) reference data. It is shown that the alignment between the reference data and the results of the RANS simulation is improved by 48% using the Spalart–Allmaras model augmented with DRL compared to the standard model. The velocity field, jet spreading rate, and axial velocity decay exhibit substantially improved agreement with both the LES reference and literature data. In addition, we applied the trained model to a jet flow with a Reynolds number of 15,000, which improved the mean field alignment by 35%, demonstrating that the framework is applicable to unseen data of the same configuration at a higher Reynolds number. Overall, this work demonstrates that DRL is a promising method for RANS closure model identification. Hurdles and challenges associated with the presented methodology, such as high numerical cost, numerical stability, and sensitivity of hyperparameters are discussed in the study.

On the Fidelity of RANS-Based Turbulence Models in Modeling the Laminar Separation Bubble and Ice-Induced Separation Bubble at Low Reynolds Numbers on Unmanned Aerial Vehicle Airfoil

The operational regime of Unmanned Aerial Vehicles (UAVs) is distinguished by the dominance of laminar flow and the flow field is characterized by the appearance of Laminar Separation Bubbles (LSBs). Ice accretion on the leading side of the airfoil leads to the formation of an Ice-induced Separation Bubble (ISB). These separation bubbles have a considerable influence on the pressure, heat flux, and shear stress distribution on the surface of airfoils and can affect the prediction of aerodynamic coefficients. Therefore, it is necessary to capture these separation bubbles in the numerical simulations. Previous studies have shown that these bubbles can be modeled successfully using the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) but are computationally costly. Also, for numerical modeling of ice accretion, the flow field needs to be recomputed at specific intervals, thus making LES and DNS unsuitable for ice accretion simulations. Thus, it is necessary to come up with a Reynolds-Averaged Navier–Stokes (RANS) equation-based model that can predict the LSBs and ISBs as accurately as possible. Numerical studies were performed to assess the fidelity of various RANS turbulence models in predicting LSBs and ISBs. The findings are compared with the experimental and LES data available in the literature. The structure of these bubbles is only studied from a pressure coefficient perspective, so an attempt is made in these studies to explain it using the skin friction coefficient distribution. The results indicate the importance of the use of transition-based models when dealing with low-Reynolds-number applications that involve LSB. ISB can be predicted by conventional RANS models but are subjected to high levels of uncertainty. Possible recommendations were made with respect to turbulence models when dealing with flows involving LSBs and ISBs, especially for ice accretion simulations.

Secondary flows in the actuator-disk simulation of wind-turbine wakes

This study explores the generation of secondary flows of Prandtl's second kind in the actuator-disk simulation of wind-turbine wakes. Leveraging large-eddy simulation data and conducting an analysis of the mean streamwise vorticity budget, we uncover the physical mechanisms contributing to this phenomenon. Our investigations attribute the emergence of such flows to the spatial gradients of the Reynolds stresses in the wake downstream of the turbines, which are, in turn, influenced by ground effects. To further investigate the phenomenon, we specifically isolate the impact of secondary flows on the wake by employing a model recognized for its incapacity to capture such dynamics: a two-equation Reynolds-averaged Navier–Stokes (RANS) model founded on the linear eddy-viscosity hypothesis. By comparing the predictions of the RANS model with those of large-eddy simulations and wind-tunnel experiments, we highlight the effect of secondary flows on the wake structure and, in particular, the upward shift of the wake. Motivated by the obtained results, we then enhance the baseline RANS model by introducing a non-linear term within the Reynolds stress tensor. This modification leads to a more accurate representation of Reynolds stresses, enabling the RANS model to capture the secondary flows in the wake. Our analysis emphasizes the importance of employing advanced RANS models in the simulation of wind farms.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

Effects of Reynolds Number On the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe = 17.8°. The Reynolds number based on the body height was varied from 5 × 103 to 5 × 104. Prior to the Reynolds number investigation, a Reynolds-Averaged Navier-Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart-Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe = 17.8° notchback Ahmed body at Re = 5 × 104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re = 1 × 104. The wake structure exhibited three regimes: symmetric (Re = 1 × 104), transitionally asymmetric (1 × 104< Re = 3.5 × 104) and fully asymmetric (Re ≤ 3.5 × 104) states. The wake asymmetry was attributed to an imbalance in entrainment from the side and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

Predictive capability of an improved AD/RANS method for multiple wind turbines and wind farm wakes

The actuator disc (AD) model combined with the Reynolds-averaged Navier-Stokes (RANS) model has been demonstrated as the most effective approach for simulating wind farm wakes due to its computational efficiency and acceptable accuracy. However, challenges remain in defining the reference inflow wind speed for the AD model and identifying a robust turbulence model for the RANS method. To solve these issues, two strategies for establishing the AD model (AD-up1D model and AD-local model), along with four turbulence models (standard k-ε, SST k-ω, linear pressure-strain RSM and modified RSM), are comprehensively validated here to predict multiple wakes within two representative wind farms. The temporal variability of multiple turbines’ power output and the significant impact of wind direction on the power is particularly emphasized. Overall, this study indicates that the proposed AD-local/Mod RSM method facilitates a realistic wake recovery in the cumulated wake flow and agrees well with the field measurements. It consistently performs well, never ranking last in any test cases, with percentage deviations ranging from 1.8% to 9.0%. Most importantly, this study evaluates the strengths and weaknesses of each AD/RANS method and provides recommendations for wind farm design purposes.

Using dispersion models at microscale to assess long-term air pollution in urban hot spots: A FAIRMODE joint intercomparison exercise for a case study in Antwerp

In the framework of the Forum for Air Quality Modelling in Europe (FAIRMODE), a modelling intercomparison exercise for computing NO2 long-term average concentrations in urban districts with a very high spatial resolution was carried out. This exercise was undertaken for a district of Antwerp (Belgium). Air quality data includes data recorded in air quality monitoring stations and 73 passive samplers deployed during one-month period in 2016. The modelling domain was 800 × 800 m2. Nine modelling teams participated in this exercise providing results from fifteen different modelling applications based on different kinds of model approaches (CFD – Computational Fluid Dynamics-, Lagrangian, Gaussian, and Artificial Intelligence). Some approaches consisted of models running the complete one-month period on an hourly basis, but most others used a scenario approach, which relies on simulations of scenarios representative of wind conditions combined with post-processing to retrieve a one-month average of NO2 concentrations.The objective of this study is to evaluate what type of modelling system is better suited to get a good estimate of long-term averages in complex urban districts. This is very important for air quality assessment under the European ambient air quality directives. The time evolution of NO2 hourly concentrations during a day of relative high pollution was rather well estimated by all models. Relative to high resolution spatial distribution of one-month NO2 averaged concentrations, Gaussian models were not able to give detailed information, unless they include building data and street-canyon parameterizations. The models that account for complex urban geometries (i.e. CFD, Lagrangian, and AI models) appear to provide better estimates of the spatial distribution of one-month NO2 averages concentrations in the urban canopy. Approaches based on steady CFD-RANS (Reynolds Averaged Navier Stokes) model simulations of meteorological scenarios seem to provide good results with similar quality to those obtained with an unsteady one-month period CFD-RANS simulations.

Improved self-adaptive turbulence eddy simulation for complex flows and stall prediction using high-order schemes

It is challenging to apply numerical simulations to accurately predict the stall behavior of aircraft equipped with high-lift devices. Simulations with Reynolds-Averaged NavierStokes (RANS) models suffer from lack of the reliability at high angles of attack with separated and reattached boundary layers, whereas wall-resolved Large Eddy Simulations (LES) of wall-bounded flows at high Reynolds numbers currently costs too much computational resources. A new unified hybrid turbulence modeling approach, denoted the Self-Adaptive Turbulence Eddy Simulation (SATES), is proposed and applied for complex turbulent flows combining with high-order numerical scheme of the Weighted Compact Nonlinear Scheme (WCNS) in the present study. It enables a seamless evolution from unsteady RANS to LES and finally approaches Direct Numerical Simulation (DNS) depending on the turbulent scales. In the framework of SATES, a new SATES-σ model with an adaptive model coefficient is developed by extending the underlying LES mode based on an enhanced sub-grid-scale model of the σ-model. The new SATES-σ is first examined in two benchmark cases of channel flow and flow past a square cylinder. Then, it is validated in supercritical flow past a circular cylinder to assess the performance of turbulent models. The results show significant improvements over the previous SATES and IDDES in the predictions of boundary layer flow. Finally, successful application is achieved in the accurate prediction of the stall of the MD-30P30N airfoil at a Reynolds number of 9×106 with wide angles of attack. The simulation results show good agreement with experimental results for surface pressure even for the challenging cases of 21 and 23 deg angles of attack. Again, the SATES-σ shows better results than the previous SATES and IDDES. The presented method has considerable potential for the challenging stall predictions.

Comprehensive comparisons of RANS, LES, and experiments over cross-ventilated building under sheltered conditions

The use of RANS (Reynolds-Averaged Navier-Stokes) simulations to study airflow over cross-ventilated buildings has been widely performed under both isolated and sheltered conditions. For a sheltered environment, great efforts still need to be made as few studies have been conducted on cross-ventilated buildings, located far downstream of the urban morphology. Therefore, in this study, a series of simulations with different turbulence models were conducted to determine the performance in predicting the external and internal airflows of a cross-ventilated building under sheltered conditions and to evaluate the ventilation performance. Two urban building dispositions were considered, namely square (SQ) and staggered (ST) layouts. The evaluation of the velocity profiles was performed in the vertical and horizontal planes of the target building to systematically determine the accuracy of each model. The qualitative results showed that several RANS models are able to generate the main features of the external (in-canyon) and internal flows. In addition, the quantitative evaluations of the internal flow showed that the vertical velocity in the vertical plane and the lateral velocity in the horizontal plane are poorly predicted in the SQ array. Furthermore, the prediction of the streamwise velocity in the horizontal plane of the ST array is not satisfactory. The RANS ventilation rates are comparable to the large-eddy simulation (LES) results for certain models in the SQ array, but the deviations are large for all models in the case of the ST array, with the highest predicted ventilation rate being 40% lower compared to LES.

Effects of arcade design on wind and thermal environment inside an idealized 2D urban canyon with realistic solar heating

The arcade design has been widely used in the architecture design since it can provide space for commercial retails and improve local thermal comfort. However, the influences of different arcade design parameters on wind and thermal environment under realistic solar heating conditions are not fully understood, which hinders further application of the arcade design. This paper aims to investigate the effects of different arcade design parameters on wind and thermal environment under different solar heating conditions. Numerical wind flow, solar radiation and heat transfer simulations of a two-dimensional deep street canyon with aspect ratio of three are performed. The steady Reynolds-Averaged Navier-Stokes model with standard k−ε turbulence model is employed in this investigation, while considering solar radiation model. Moreover, the realistic solar heating simulations are achieved by setting different local solar times, i.e., LST0900 (leeward wall heating), LST1200 (street ground heating) and LST1500, (windward wall heating). Under realistic solar heating conditions, the building wall heating and the street ground heating are shown to evidently influence the strength and location of the predominant recirculation inside the street canyon, especially for the windward wall heating. Moreover, analysis results have shown that the arcade width has larger influences on wind and thermal environment than that of the arcade height. Particularly, the wind velocity increases 2.1 to 3.8 times, the air temperature decreases 0.42–2.24 °C and the Physiological Equivalent Temperature value drops between 2.2 °C and 7.0 °C when the arcade width increases to half of building width.

Eddy–Viscosity Reynolds-Averaged Navier–Stokes Modeling of Air Distribution in a Sidewall Jet Supplied into a Room

Air velocity is one of the key parameters affecting the sensation of thermal comfort. In mixing ventilation, the air is most often supplied above the occupied zone, and the air movement in a room is caused by jets that generate recirculating flows. An effective tool for predicting airflow in a room is CFD numerical modeling. In order to reproduce the air velocity distribution, it is essential to select a proper turbulence model. In this paper, seven Eddy–Viscosity RANS turbulence models were used to carry out CFD simulations of a sidewall air jet supplied into a room through a wall diffuser. The goal was to determine which model was the most suitable to adopt in this type of airflow. The CFD results were validated using experimental data by comparing the gross and integral parameters, along with the parameters of the quasi-free jet model. The numerical results obtained for Std k-ε and EVTM models were most consistent with the measurements. Their error values slightly exceeded 15%. On the contrary, the k-ω and RNG k-ε models did not reproduce the quasi-free jet parameters correctly. The research findings can prove beneficial for simulating air distribution in supplied air jets during the initial conceptual phases of HVAC system design.

Simulation of supersonic axisymmetric base flow with a data-driven turbulence model

Axisymmetric base flow involves massive flow separation which is challenging for a typical Reynolds-averaged Navier-Stokes (RANS) turbulence model. Furthermore, a supersonic condition imposes additional difficulties to a turbulence model in predicting strong compressibility effects associated with the flow separation phenomena. A data-driven approach is pursued here to improve a turbulence model. The Spalart-Allmaras model is corrected from an optimization process, and then the model correction is mapped to local flow features through a machine learning process. For the optimization-combined machine learning method, the field inversion and machine learning framework is adapted here with three major modifications. First, a zonal-field inversion method is suggested to avoid the undesired modification of attached flow in the optimization process for the model correction. Second, the RANS model is modified by adjusting a net balance between the production and destruction terms in the RANS equation. Third, the local Mach number is included in the machine learning process to incorporate compressibility effects of the supersonic flow. The current study indicates that the improved RANS model reduces the eddy viscosity in the separated region, compared to the baseline RANS model. The reduction of the eddy viscosity helps to predict the base expansion of the supersonic flow and the size of the recirculation region. Current computations are compared with relevant literature data including wake velocity profiles and the base pressure in the wide range of the supersonic Mach number.

Adjoint Design Optimization Under the Uncertainty Quantification of Reynolds-Averaged Navier-Stokes Turbulence Model

Considering the structural uncertainties of Reynolds-averaged Navier–Stokes (RANS) models, a design optimization method under eigenspace perturbations of the RANS model has been proposed for aerodynamic applications. Optimized geometries with confidence intervals with improved performance have been obtained for U-pipe, Busemann airfoil, and supersonic separator. The perturbations are injected into the eigenvalues and eigenvectors of turbulence anisotropic tensors nonuniformly and adaptively; thus, the uncertainty interval of the RANS model is obtained by six simulations. The adjoint method is employed to perform single-objective optimization on three physical models based on uncertainty quantification. The geometric profiles before and after optimization are presented, and the area surrounded by different profiles reflects the differences in geometric optimization caused by the uncertainty of the model form. Shape optimization within the confidence interval achieves enhanced performance with robust improvements, reducing the sensitivity to manufacturing tolerances. Design optimization under the framework of uncertainty quantification may have great practicability as an engineering application tool.

Swash-flow induced forces on human body standing on a smooth and impermeable slope: A numerical study with experimental validations

ABSTRACT Swash flow poses a significant hazard to pedestrians standing on the slope of the seawall. Unlike the forces of overtopping flow or open channel flow on the human body, which have been studied before, swash flow has two distinct cycles within one wave period: onshore flow and offshore flow. Both cycles can risk human safety by exerting hydrodynamic forces on the body. This paper presents a numerical study to examine the hydrodynamic forces exerted on the human body when subjected to swash flow on a smooth and impermeable slope. A Reynolds-averaged Navier-Stokes (RANS) model is set up in OpenFOAM, where the numerical results are compared with experimental data obtained from wave tank tests. Reasonable agreement has been achieved, which validates the numerical model. We examine the kinematics of swash flow generated by plunging and surging breakers. In the case of a plunging breaker, we observe that the instantaneous runup height exhibited asymmetry, whereas it is nearly symmetric for a surging breaker. The velocity profile is then used to compute the momentum flux of the swash flow, which is shown to be associated with the inline forces exerted on the human body. We have defined an instability index to assess the risk of pedestrian mobilisation by swash flow, demonstrating its dependence on the Iribarren number and the body's position. The analysis reveals that the associated risk is substantially reduced as the Iribarren number increases and when the body moves towards the shoreline.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.