Reynolds-averaged Navier-Stokes Turbulence Models Research Articles

Simplified Polynomial-asymptotic-distribution Actuator Disc (SPAD) method for wind turbine wake simulation based on k-[formula omitted]-[formula omitted] turbulence model

In large wind farms, wake effect has a negative impact on the annual production of wind turbines. As a result, wind turbine wake simulation is important for wind farm micro-sitting to minimize power loss and maximize energy production. Coupled with Reynolds Averaged Navier–Stokes turbulence model, Simplified Uniform-distribution Actuator Disc method is the most widely-used rotor model for wake simulation in engineering practice. The conventional simplified uniform-distribution actuator disc models suffer discrepancies of wake velocity prediction compared with the measurements in the near wake region. The novelty of the current research is to propose a Simplified Polynomial-asymptotic-distribution Actuator Disc method based on k−ϵ−fP turbulence model for cylindrical actuator disc cell region with finite thickness, which is simple for implementation and improves the accuracy of wake simulation compared with conventional method. The proposed method conforms to momentum conservation and is as simple as conventional method because of its polynomial formulation and no requirement for aerodynamics data in Generalized Actuator Disc model. From the verification and validation cases, it can be found that the proposed model has better agreement with both high-fidelity actuator line model and the field test measurements from Lillgrund wind farm compared with conventional model. The proposed actuator disc model has the potential to be applied to the micrositting of large offshore wind farms in the future.

Evaluation of Reynolds-averaged Navier-Stokes turbulence models in open channel flow over salmon redds

Evaluation of Reynolds-averaged Navier-Stokes turbulence models in open channel flow over salmon redds

Assessment of RANS turbulence models based on the cell-based smoothed finite element model for prediction of turbulent flow

There is a growing body of literature that recognizes the importance of Smoothed Finite Element Method (S-FEM) in computational fluid dynamics (CFD) fields and, to a lesser extent, in complex turbulent flow problems. This study evaluates the performance of Reynolds-averaged Navier-Stokes (RANS) turbulence models within the S-FEM framework for predicting incompressible turbulent flows. Our assessment of three turbulence models based on the cell-based S-FEM (CS-FEM) is convincingly supported by testing on three flow problems. It is found that the CS-FEM exhibits superior mesh robustness compared to the Finite Volume Method (FVM) and achieves higher computational accuracy than the Finite Element Method (FEM). Notably, the CS-FEM combined with the standard k-epsilon model (CS-FEM-SKE) and the realizable k-epsilon model (CS-FEM-RKE) demonstrate robust performance in handling severely distorted meshes, with CS-FEM-RKE outperforming in regions of strong flow separation and convection. The Spalart-Allmaras model with CS-FEM (CS-FEM-SA) offers faster computational speed but shows poor mesh robustness. The hexcore mesh based on CS-FEM-RKE is employed to evaluate the aerodynamic performance of High-speed train (HST), resulting in enhanced computational efficiency. The outcomes show good agreement with other numerical studies and experimental data. Overall, it also highlights the latent capability of CS-FEM in solving complex engineering problems.

Effect of tip-gap height on tip-leakage flows in a stationary NACA hydrofoil

ABSTRACT This paper presents a numerical study on the tip-leakage flow (TLF) for distinct tip-gap heights of a stationary hydrofoil. Steady-state simulations using the Reynolds-averaged Navier–Stokes turbulence model were performed to evolve the computations. The extensions of the tip-leakage vortex (TLV) and tip-separation vortices (TSVs) increased for larger tip-gap heights. Conversely, additional vortices were yielded for the smallest gap height evaluated. The lower coefficient of the minimum pressure value in the TLV was observed for the larger tip-gap heights. A downward flow region expanded with a higher peak value near the TSVs on the suction side for the larger tip gap. Thus, the spin of the TLV could be further strengthened. The low velocity flow in the boundary layer was entrained into the TLV for the smaller tip gap, whereas the low-turbulence flow in the mainstream crossed the gap and was entrained into the TLV for the larger tip gap.

Bayesian interface technique-based inverse estimation of closure coefficients of standard k−ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier–Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k−ϵ RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k−ϵ turbulence model are calibrated among the five coefficients ( Cμ,Cϵ1,Cϵ2,σϵ and σ k ). The Bayesian inference technique using the Metropolis–Hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x/h=2 and x/h=4 , along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k−ϵ turbulence model (baseline). The deviation of calibrated C µ is almost 50%–60% from baseline and for Cϵ1 and Cϵ2 it is 3%–12% and 6%–9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.

Turbo-RANS: straightforward and efficient Bayesian optimization of turbulence model coefficients

PurposeIndustrial simulations of turbulent flows often rely on Reynolds-averaged Navier-Stokes (RANS) turbulence models, which contain numerous closure coefficients that need to be calibrated. This paper aims to address this issue by proposing a semi-automated calibration of these coefficients using a new framework (referred to as turbo-RANS) based on Bayesian optimization.Design/methodology/approachThe authors introduce the generalized error and default coefficient preference (GEDCP) objective function, which can be used with integral, sparse or dense reference data for the purpose of calibrating RANS turbulence closure model coefficients. Then, the authors describe a Bayesian optimization-based algorithm for conducting the calibration of these model coefficients. An in-depth hyperparameter tuning study is conducted to recommend efficient settings for the turbo-RANS optimization procedure.FindingsThe authors demonstrate that the performance of the k-ω shear stress transport (SST) and generalized k-ω (GEKO) turbulence models can be efficiently improved via turbo-RANS, for three example cases: predicting the lift coefficient of an airfoil; predicting the velocity and turbulent kinetic energy fields for a separated flow; and, predicting the wall pressure coefficient distribution for flow through a converging-diverging channel.Originality/valueTo the best of the authors’ knowledge, this work is the first to propose and provide an open-source black-box calibration procedure for turbulence model coefficients based on Bayesian optimization. The authors propose a data-flexible objective function for the calibration target. The open-source implementation of the turbo-RANS framework includes OpenFOAM, Ansys Fluent, STAR-CCM+ and solver-agnostic templates for user application.

Numerical Analysis into the Improvement Performance of Ducted Propeller by using Fins: Case Studies on Types B4-70 and Ka4-70

Numerical analysis was conducted to assess the impact of fins on the B4-70 and Ka4-70 propeller performance. The study explored different fin variations, specifically bare fins, Propeller Boss Cap Fins (PBCF), and propeller nozzles, using computational fluid dynamics (CFD) simulations. To obtain the best results, the researchers utilized the explicit algebraic stress model (EASM) based on Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence modelling. The primary goal of this study was to improve the energy efficiency of ships by examining various propeller configurations, both open and ducted. The overall conclusions indicated that the B4-70 PBCF convergent and Ka4-70 PBCF divergent with the addition of nozzle 19A exhibited the highest efficiency based on the EASM analysis. The CFD simulation results for both B4-70 and Ka4-70 propellers, utilizing a nozzle 19A with added boss cap fins, revealed several noteworthy phenomena. Firstly, for the B4-70 propeller, efficiency (η0) at J = 0.6 to J = 0.8 showed an increase of 1% to 2%. Secondly, concerning the Ka4-70 propeller, efficiency (η0) at J = 0.6 to J = 0.8 increased by 2% to 10%. These findings clearly demonstrate that the use of an ESD, such as the nozzle 19A with added boss cap fins, enhances the propulsion performance of the ship. It is evident that the CFD approach remains suitable and reliable for overall simulations.

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Errors and uncertainties in CFD validation for non-equilibrium turbulent boundary layer flows at high Reynolds numbers

NATO AVT-RTG-349 was dedicated to the validation of computational fluid dynamics (CFD) methods based on the Reynolds-Averaged Navier-Stokes (RANS) equations and statistical turbulence models for non-equilibrium turbulent-boundary-layer flows at high Reynolds numbers. This paper describes and discusses the errors and uncertainties arising in the comparison of RANS simulation results with experimental data from wind-tunnel experiments. These errors and uncertainties are associated with the CFD grid and the discretization, the physical modelling, the measurement accuracy, and the differences in the flow conditions between the experimental facility and the computational set-up. The results show the need for a grid-convergence study using systematically-refined families of CFD grids. The two major sources of errors are the RANS turbulence model and the uncertainty originating from the differences between the computational set-up and the wind-tunnel. Then two possible paths for future research are described: future CFD mesh generation, and future validation experiments at high Reynolds numbers.

Influence Evaluation of Open Propellers with Boss Cap Fins: Case Studies on Types B4-70 and Ka4-70

Numerical analysis of fins effect on propeller performance was conducted, specifically using the B4-70 and Ka4-70 propellers. The study investigated different types of fins, including bare fins and PBCF (Propeller Boss Cap Fins) using computational fluid dynamics (CFD) simulations. The explicit algebraic stress model (EASM) based on Reynolds-Averaged Navier-Stokes (RANS) equations and turbulence modeling was employed to determine the optimal results. The main objective of this research was to enhance energy efficiency in ships by examining various open propeller configurations. The CFD simulation results for open propellers B4-70 and Ka4-70, with the addition of boss cap fins, revealed interesting phenomena. When the open propellers B4-70 and Ka4-70 were equipped with PBCF, they would experience an increase in efficiency (η0). This was because the performance of the fins functioned optimally when the advance ratio (J) is high, as evident from the high velocity values. Thus, with higher velocity and lower pressure in the boss cap region at high J values, there was an elevation in thrust force due to the reduction of hub vortex. In the case of open propeller B4-70 with added PBCF, there was an increase in the efficiency value (η0) ranging from 3% to 5% when J varied from 0 to 0.7. Similarly, for propeller Ka4-70 with the addition of PBCF, there was an increase in the efficiency value (η0) ranging from 1% to 3% when J varied from 0 to 0.7. Notably, the use of an Energy-Saving Device (ESD) in the form of PBCF can increase the efficiency of ship propeller, as reported in this paper. Consequently, these findings affirmed the reliability of the overall calculations using the CFD approach.

Impact of modelling assumptions in cavitating flow of simplified injector

Here, three-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations are employed for in-nozzle flow modelling. The aim is to evaluate the capabilities and sensitivities of simulating in-nozzle flow phenomena by using homogeneous phase change models. Two commonly used homogeneous models are employed – (i) Homogeneous Equilibrium Model (HEM) and (ii) Homogeneous Relaxation Model (HRM) A simplified nozzle with reference experimental data is modelled in the developing, super cavitation, and hydraulic flip regimes using OpenFOAM. The influence of the inlet boundary condition and turbulence models are investigated. With HEM, three barotropic compressibility models are tested. The research seeks to understand the strengths and limitations of each approach by comparing different sub-models and their interactions with the flow fields and phase change phenomena. Ultimately, this study contributes to a better understanding of how different modelling choices can influence the accuracy and reliability of cavitation simulations using homogeneous phase change models. While the simulations demonstrated reliable predictions for low-order velocity statistics, substantial discrepancies were identified in the prediction of the cavitating region by both homogeneous models. Additionally, the relaxation model predicted only minor cavitation. In contrast, acceptable flow predictions were achieved using different barotropic compressibility models and inlet boundary condition types, as well as most RANS turbulence models, where the RNG k-ɛ model deviated more from the other turbulence models. Therefore, the added value of the present study is summarised as: (a) Four different cavitation regimes are simulated with HEM and HRM in a single study. (b) The more comprehensive HRM approach does not produce better velocity or cavitation predictions for a low-speed flow using the default relaxation time. (c) The choice of turbulence model can radically affect the cavitation prediction, in addition to velocity fields. (d) The HEM flow simulation has little sensitivity to the barotropic compressibility model.

Numerical modelling of continuous casting of round billets with turbulence in the melt

The present work aims to solve the continuous casting benchmark problem in axisymmetry with turbulence in the melt by the meshless method. The physical model of the liquid-solid system that involves mass, momentum and energy conservation is formulated in the mixture continuum approximation. The melt is assumed Newtonian and incompressible. A k-epsilon Reynolds averaged Navier-Stokes turbulence model is implemented with Abe-Kondoh-Nagano closures. The mushy region is modelled as a Darcy porous media with the Kozeny-Carman permeability model. The solution of partial differential equations is implemented locally using collocation with radial basis functions and explicit time-stepping. The velocity pressure coupling is performed using the fractional step method. The validation of the model is assessed by comparing its outcomes with the results of the finite volume method. A sensitivity study of the varying casting speed and temperature on the velocity, temperature, and solid fraction fields is shown.

Development of a Benchmark for Thermal Striping in Gas-Cooled Fast Reactors

This paper presents the development of a benchmark for predicting thermal striping through simulation. This work utilized large eddy simulation and will be used to benchmark future models. The testing domain was created using both the STRUCT and the Reynolds-averaged Navier-Stokes turbulence models and is based on an earlier design of the General Atomics Fast Modular Reactor upper plenum. The plenum features two adjacent, identical hexagonal bundles each with a center-placed axial rod drive, with a hot left coolant stream and a cold right coolant stream. The simulation solves the nondimensional Navier-Stokes equations, with temperature accounted as a passive scalar. First- and second-order flow statistics were obtained after 600 convective time units of averaging. The first-order statistics reveal that the hot jet is damped by a recirculatory flow from the near wall. At the same location, the second-order statistics show strong oscillations both in velocity and temperature. The power spectral density was utilized to determine that a low-frequency oscillation occurs here that is within the range of interest for thermal striping. Furthermore, proper orthogonal decomposition was used to identify coherent structures that confirm the oscillatory behavior, indicative of thermal striping. Overall, this benchmark can aid in the development of future models for predicting thermal striping in nuclear reactors, potentially leading to improved reactor safety and performance.

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.

Reynolds-average Navier-Stokes turbulence models assessment: A case study of CH4/H2/N2-air reacting jet

Computational Fluid Dynamics has become a very powerful tool for developing engineering combustion devices, such as burners and furnaces. However, there are a wide variety of turbulence models, and some of them have proven to be more effective for some turbulent flow configurations than others. A reacting turbulent jet is a common flow configuration found in combustion engineering devices like burners. The present work assesses Reynolds-Average Navier-Stokes turbulence models, being tested on a CH4/H2/N2-Air reacting jet. Eight two-equation eddy-viscosity and three five-equation turbulence models were tested in the studied turbulent flow. Computational results were compared against experimental measurements in terms of flow field variables, mean mixture fraction, temperature, and species mass fraction. The findings suggest a strong influence of the turbulence model perforce on the mean mixture fraction as well as on the turbulence-chemistry interaction model. The modified version of the standard k-ε model proves to be the more reliable choice for this reactive flow configurations. Specially, where the flow patterns of the jet dictate the general flow physics. Near the fuel nozzle, both the Reynolds stress model with stress baseline k-ω (RSM-SBSL) and the standard k-ω model exhibit better agreement with experimental data than the conventional modified k-ε model. Moreover, findings from the standard modified k-ε model indicate a significant underestimation of spreading rates for radial samples in regions where jet spreading intensifies.

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.

Characteristics Investigations of Ducted Ka4-70 Series Propeller with Boss Cap Fins Using Numerical and Experimental Method

Unconventional system that are generally adopted for ship propulsion are Ducted Propellers. These devices have recently been studied with medium-fidelity computational fluid dynamics code (based on the potential flow hypothesis) with promising results. Numerical and experimental comparison of ducted propeller with PBCF, case studies with Propeller Ka4-70 used combination ducted and PBCF Divergent. The study was done numerically using computational fluid dynamics (CFD) approach. The solver is based on the Reynolds-Averaged Navier-Stokes (RANS) solutions and turbulence modelling explicit algebraic stress model (EASM). The test data was obtained from CFD simulations consisting of the open propeller and combination Nozzle plus PBCF, but the experiment was done to Nozzle and PBCF only. All measurements were carried out from J = 0 to J = 1.0 with speeds from 0 m/s to 2.445 m/s. The results of the comparative investigation cases between numerical and experiment analysis from Ka4-70 propellers with Nozzle 19A and PBCF Divergent appears that between CFD and experiments, several phenomena are seen. (i) the Ka4-70 propeller without Nozzle 19A and PBCF divergent experienced large pressure at low-speed J = 0.1 to high-speed J = 0.7, but Ka4-70 propeller with Nozzle and PBCF divergent reach highest pressure at J = 0.1 to J = 0.5; (ii) the Ka4-70 propeller without 19A nozzle and PBCF divergent increases the flow velocity at the boss cap fins but does not increase the axial induce velocity, while Ka4-70 propeller using nozzle and PBCF divergent increases the axial induce velocity of the blade, but does not increase the flow velocity of the boss cap fins; (iii) Ka4-70 propeller without Nozzle and PBCF value increase of propeller η0 to 12% when ESD added in the form of Nozzle and PBCF when J is high, from J = 0.7 to J = 1.0. ; (iv) Ka4-70 propellers with Nozzle 19A and PBCF Divergent has very similar η0 from J=0 to J=1.0. CFD approach are still appropriate to be relied upon for the overall simulation.

Numerical Investigations of Turbulent Flow Through A 90-Degree Pipe Bend And Honeycomb Straightener

Abstract Pipe bends are commonly used in piping systems in offshore and subsea installations. The present study explores the design considerations for the honeycomb straightener inserted downstream of a 90-degree pipe bend. The objective of the study is to evaluate the effectiveness of the honeycomb in suppressing the flow swirling for different distances from the bend outlet (Lb) and different values of the honeycomb thickness (t). The turbulent flow through the 90-degree circular pipe bend with the honeycomb straightener is investigated by carrying out numerical simulations using the Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling approach. The Explicit Algebraic Reynolds Stress Model (EARSM) is adopted to resolve the Reynolds stresses. The honeycomb thickness to pipe diameter ratio (t/D) is varied between 0.1 and 1. The normalized distance from the bend outlet to the honeycomb straightener (Lb/D) is varied between 1 and 5. The disturbance in the velocity field is generated by the pipe bend with the curvature radius to pipe diameter ratio (Rc/D) of 2 and Reynolds number (Re) of 2×105. It is found that both the increase in Lb/D and t/D improves the performance of the device in removing the swirl behind the bend outlet. The best performance is observed for the honeycomb straightener with the distance Lb/D=5 and thickness t/D=0.5.

Effect of void space arrangement on wind power potential and pressure coefficient distributions for high-rise void buildings

High-rise void building complexes can augment the permeation of airflows over buildings, and thereby strengthen urban wind energy harvesting for realization of the sustainable development goals (SDGs). This paper considers the wind over a typical 2×2 compact high-rise building array with the openings to analyze the wind power potential at varying void sizes, locations of voids, and direction of incoming wind. The predicted mean wind speeds and turbulence intensities are compared against the measured data with 4 generic high-rise building models having voids in an atmospheric boundary layer wind tunnel for validation of the computational model. Based on the comparative results from four common Reynolds-averaged Navier-Stokes (RANS) turbulence models including the standard, realizable, renormalization group (RNG) k-ε, and shear-stress transport (SST) k-ω models as well as the Reynolds stress model (RSM), the RSM approach can provide the most accurate predictions of streamwise mean velocity and turbulence intensity. The present study then conducts CFD simulations to explore the effects of opening configuration and wind direction on the wind field around high-rise void buildings. Considering the variations of void sizes of 10 × 10 m2, 12.5 × 12.5 m2, 15 × 15 m2, void heights of z/H = 0.25, 0.5, 0.75 and wind directions of 0°, 45°, respectively, the simulated results indicate elevated wind power densities with acceptable turbulence intensities over the upstream gap passage and void channels to achieve prospective urban wind power harvest and mitigate wind load on structures of high-rise void buildings.

CFD modelling of initial stages of dam-break flow

Cases of dam failures are seen almost every year globally, and the propagation of rapidly varying unsteady flows resulting from those dam failures has significant environmental and economic consequences. A three-dimensional Computational Fluid Dynamics model was created to solve unsteady Reynolds-Averaged equations to investigate the generation and propagation of dam-break flows and reflected flood waves in the presence of a trapezoidal bottom obstacle. The dam-breaks were modelled using OpenFOAM based on the Volume of Fluid method employing the Finite Volume Method, and the performance of various Reynolds-Averaged Navier-Stokes turbulence models, including the realizable k − ε, SST k − ω (Shear Stress Transport k − ω), and v2 − f models, has been evaluated. To assess the capabilities of the different turbulence models, quantitative comparisons of numerical simulations with laboratory experiments were completed, and it was found that the SST k − ω model performed better in predicting the free surface profiles and negative bore propagation speeds than the realizable k − ε and v2 − f models.