Reynolds-averaged Navier-Stokes Turbulence Models Research Articles

Comparison of Reynolds average Navier–Stokes turbulence models in numerical simulations of the DC arc plasma torch

Five turbulence models of Reynolds average Navier–Stokes (RANS), including the standard model, the RNG model taking into account the low Reynolds number effect, the realizable model, the SST model, and the Reynolds stress model (RSM), are employed in the numerical simulations of direct current (DC) arc plasma torches in the range of arc current from 80 A to 240 A and air gas flow rate from 10 m3 h−1 to 50 m3 h−1. The calculated voltage, electric field intensity, and the heat loss in the arc chamber are compared with the experiments. The results indicate that the arc voltage, the electric field, and the heat loss in the arc chamber calculated by using the standard model, the RNG model taking into account the low Reynolds number effect, and the realizable model are much larger than those in the experiments. The RSM predicts relatively close results to the experiments, but fails in the trend of heat loss varying with the gas flow rate. The calculated results of the SST model are in the best agreement with the experiments, which may be attributed to the reasonable predictions of the turbulence as well as its distribution.

Turbulence Modeling for Turbulent Boundary Layers at Supercritical Pressure: A Model for Turbulent Mass Flux

Based on the analysis of the direct numerical simulation (DNS) database of the heated and unheated turbulent boundary layers at supercritical pressures (Kawai J. Fluid Mech. 865, 563 2019), this paper proposes a Reynolds-averaged Navier-Stokes (RANS) turbulence modeling for predicting the turbulent boundary layers at supercritical pressure where large density fluctuations are induced by the pseudo-boiling phenomena. The proposed approach is to model the mass flux contribution term $M_{\tau }=\overline {u_{i}^{\prime \prime }} \partial \overline {\tau _{ij}}/\partial x_{j}$ in the turbulent kinetic energy equation (more specifically the turbulent mass flux $\overline {u_{i}^{\prime \prime }}= -\overline {\rho ^{\prime } u_{i}^{\prime }}/\overline {\rho }$ in Mτ term) and add the modeled Mτ to the k-transport equation in the RANS model in order to incorporate the effects of the large density fluctuations on turbulence observed in the DNS. The key idea of modeling the turbulent mass flux in Mτ is to employ the gradient diffusion hypothesis and we propose to model $\overline {u_{i}^{\prime \prime }}$ as a function that is proportional to the density gradient (i.e. $\overline {u_{i}^{\prime \prime }} \propto \overline {\mu }_{t} \partial \overline {\rho }/\partial x_{j}$). The proposed RANS model shows significant improvements over existing models for predicting the logarithmic law for the mean velocity and temperature in the turbulent boundary layers at supercritical pressure, something that existing RANS models fail to do robustly.

Eulerian CFD modeling of nozzle geometry effects on ECN Sprays A and D: assessment and analysis

Diesel spray modeling is a multi-scale problem with complex interactions between different flow regions, that is, internal nozzle flow, near-nozzle region and developed spray, including evaporation and combustion. There are several modeling approaches that have proven particularly useful for some spray regions although they have struggled at other areas, while Eulerian modeling has shown promise in dealing with all characteristics at a reasonable computational effort for engineering calculations. In this work, the [Formula: see text]–Y single-fluid diffuse-interface model, based on scale separation assumptions at high Reynolds and Weber numbers, is used to simulate the engine combustion network Sprays A and D within a Reynolds-averaged Navier–Stokes turbulence modeling approach. The study is divided into two parts. First of all, the larger diameter Spray D is modeled from the nozzle flow till evaporative spray conditions, obtaining successful prediction of numerous spray metrics, paying special attention to the near-nozzle region where spray dispersion and interfacial surface area can be validated against measurements conducted at the Advanced Photon Source at Argonne National Laboratory, including both the ultra-small-angle X-ray scattering and the X-ray radiography. Afterwards, an analysis of the modeling predictions is made in comparison with previous results obtained for Spray A, considering the nozzle geometry effects in the modeling behavior.

Modern discontinuous Galerkin methods for the simulation of transitional and turbulent flows in biomedical engineering: A comprehensive LES study of the FDA benchmark nozzle model.

This work uses high-order discontinuous Galerkin discretization techniques to simulate transitional and turbulent flows through medical devices. Flows through medical devices are characterized by moderate Reynolds numbers and typically involve different flow regimes such as laminar, transitional, and turbulent flows. Previous studies for the FDA benchmark nozzle model revealed limitations of Reynolds-averaged Navier-Stokes turbulence models when applied to more complex flow scenarios. Recent works based on large-eddy simulation approaches indicate that these limitations can be overcome but also highlight potential limitations due to a high sensitivity with respect to numerical parameters. The methodology presented in this work introduces two novel ingredients compared with previous studies. Firstly, we use high-order discontinuous Galerkin methods for discretization in space. The inherent dissipation and dispersion properties of high-order discontinuous Galerkin discretizations are expected to render this approach well suited for transitional and turbulent flow simulations. Secondly, to mimic blinded CFD studies, we propose to use a precursor simulation approach in order to predict the inflow boundary condition for laminar, transitional, and turbulent flow regimes instead of prescribing analytical velocity profiles at the inflow. We investigate the whole range of Reynolds numbers as suggested by the FDA benchmark nozzle problem and compare the numerical results to experimental data obtained by particle image velocimetry in order to critically assess the predictive capabilities of the solver on the one hand and the suitability of the FDA nozzle problem as a benchmark in computational fluid dynamics on the other hand.

Optimization of RANS turbulence models using genetic algorithms to improve the prediction of wind pressure coefficients on low-rise buildings

Being associated with natural ventilation, the pressure distribution on surfaces is relevant for energy consumption, thermal comfort, and air quality in buildings. The aim of this work is to present a simulation-based optimization methodology to recalibrate the closure coefficients of Reynolds-averaged Navier-Stokes (RANS) turbulence models in order to improve the prediction of wind surface-averaged pressure coefficients on a wide range of isolated low-rise buildings. To accomplish this, genetic algorithms and Computational Fluid Dynamics (CFD) simulations are dynamically coupled to find the closure coefficients set which minimize the CFD prediction error regarding wind-tunnel experimental data. The methodology is applied to two turbulence models, the renormalization group k-epsilon model (RNG) and the Spalart-Allmaras model (SA), considering as target cases buildings with different roof types (flat, gable and hip) and wind incidence angles. In order to show the strength of the novel optimal sets of closure coefficients obtained, an exhaustive validation is performed over other low-rise buildings (52 new cases) which were not calibrated against. Results validate using the optimal sets because the recalibrated RNG and SA models decrease the prediction error between 11-64% and 8–45%, respectively, regarding using the standard ones.

Turbulence Modeling Effects on the CFD Predictions of Flow over a Detailed Full-Scale Sedan Vehicle

In today’s road vehicle design processes, Computational Fluid Dynamics (CFD) has emerged as one of the major investigative tools for aerodynamics analyses. The age-old CFD methodology based on the Reynolds Averaged Navier–Stokes (RANS) approach is still considered as the most popular turbulence modeling approach in automotive industries due to its acceptable accuracy and affordable computational cost for predicting flows involving complex geometries. This popular use of RANS still persists in spite of the well-known fact that, for automotive flows, RANS turbulence models often fail to characterize the associated flow-field properly. It is even true that more often, the RANS approach fails to predict correct integral aerodynamic quantities like lift, drag, or moment coefficients, and as such, they are used to assess the relative magnitude and direction of a trend. Moreover, even for such purposes, notable disagreements generally exist between results predicted by different RANS models. Thanks to fast advances in computer technology, increasing popularity has been seen in the use of the hybrid Detached Eddy Simulation (DES), which blends the RANS approach with Large Eddy Simulation (LES). The DES methodology demonstrated a high potential of being more accurate and informative than the RANS approaches. Whilst evaluations of RANS and DES models on various applications are abundant in the literature, such evaluations on full-car models are relatively fewer. In this study, four RANS models that are widely used in engineering applications, i.e., the realizable k − ε two-layer, Abe–Kondoh–Nagano (AKN) k − ε low-Reynolds, SST k − ω , and V2F are evaluated on a full-scale passenger vehicle with two different front-end configurations. In addition, both cases are run with two DES models to assess the differences between the flow predictions obtained using RANS and DES.

Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow

Eigenmodes of averaged small-amplitude perturbations to a turbulent channel flow – which is one of the most fundamental canonical flows – are identified for the first time via an extensive set of high-fidelity graphics processing unit accelerated direct numerical simulations. While the system governing averaged small-amplitude perturbations to turbulent channel flow remains unknown, the fact such eigenmodes can be identified constitutes direct evidence that it is linear. Moreover, while the eigenvalue associated with the slowest-decaying anti-symmetric eigenmode mode is found to be real, the eigenvalue associated with the slowest-decaying symmetric eigenmode mode is found to be complex. This indicates that the unknown linear system governing the evolution of averaged small-amplitude perturbations cannot be self-adjoint, even for the case of a uni-directional flow. In addition to elucidating aspects of the flow physics, the findings provide guidance for development of new unsteady Reynolds-averaged Navier–Stokes turbulence models, and constitute a new and accessible benchmark problem for assessing the performance of existing models, which are used widely throughout industry.

A Detailed Study of Row-Trenched Holes at the Combustor Exit on Film-Cooling Effectiveness

Abstract To analyse the effects of cylindrical- and row-trenched cooling holes with an alignment angle of 90 degrees on the film-cooling effectiveness near the combustor end wall surface at a blowing ratio of 3.18, the current research was done. This research included a 3D representation of a Pratt and Whitney gas turbine engine, which was simulated and analysed with a commercial finite volume package FLUENT 6.2.26. The analysis was done with Reynolds-averaged Navier–Stokes turbulence model on internal cooling passages. This combustor simulator was combined with the interaction of two rows of dilution jets, which were staggered in the streamwise direction and aligned in the spanwise direction. In comparison with the baseline case of cooling holes, using row-trenched hole near the end wall surface increased the film-cooling effectiveness 44% in average.

Impact of the volume heat source on the RANS-based CFD analysis of Molten Salt Reactors

Several efforts have been spent in recent years to address the simulation challenges posed by the non-conventional design of Molten Salt Reactors (MSRs). One of the design specificities of MSRs is the volume heat source in the liquid fuel, which has been proven by various authors to significantly alter the heat transfer processes in these reactors. This paper focuses on the impact of a volume heat source on the wall treatment of the standard high-Reynolds Reynolds-Averaged Navier Stokes (RANS) turbulence models. A modified thermal wall function is derived and its impact is discussed for typical MSR calculations. The results show a non-negligible impact on graphite temperatures, both at steady state and during transients.

Reynolds-averaged Navier–Stokes modelling in transonic S-ducts with passive flow control

S-duct diffusers are used in aircraft with embedded engines to route ambient air to the fan face. Sizing and stealth considerations drive a need for high curvature ducts, but the curvature causes complex secondary flows that lead to total pressure distortion and swirl velocities at the engine face. These must be controlled for stable engine operation. In this paper, tubercles, a novel bio-inspired passive flow control method, are analysed numerically in a duct with transonic flow. The results are compared to experimental data obtained as part of a campaign at the Royal Military College, Canada to investigate the effects of S-duct geometry and novel passive flow control devices on the performance of transonic S-ducts. The performance of Reynolds-averaged Navier–Stokes turbulence models in the S-ducts is assessed – Menter's shear stress transport model predicts excessive losses due to the overactivity of its stress limiter. The realisable k–ɛ model gives a significant improvement in the prediction of static pressure distributions, but losses and distortion characteristics are predicted poorly due to the model's inability to resolve the effects of unsteadiness in separated regions. Large tubercle geometries are found to trigger earlier separation in the centre of the duct by concentrating low momentum fluid in valleys, but they also act as boundary layer fences away from the duct centre. Smaller geometries are found to generate vortices that re-energise the boundary layer, delaying flow separation. Methods are recommended for future computational analyses of S-ducts and new designs of tubercles.

Laminar-turbulent transition in a constricted tube: Comparison of Reynolds-averaged Navier–Stokes turbulence models and large eddy simulation with experiments

Constricted tubes appear in many engineering as well as biological systems such as blood vessels or pulmonary airways. The aim of this article is to test the ability of different turbulence models to predict the flow field and deposition of particles in a constricted tube. The constricted geometry of Ahmed and Giddens was employed to compare various numerical approaches. Two large eddy simulations and several Reynolds-averaged Navier–Stokes models were used for calculations using the Star-CCM+ commercial solver. The performance of these models was compared with the experiments and other published studies. For selected turbulence models, deposition of particles with different Stokes numbers using Lagrangian multiphase model was enabled. The results show that large eddy simulation best predicts the transition from laminar to turbulent flow in terms of mean axial velocity, and similarly does also standard low-Reynolds k–ε model. The comparison of deposition fractions shows substantial differences among the models, especially for the smallest particles. It was demonstrated that even a simple stenosed smooth tube is a very intricate problem for the present computational fluid dynamics models; therefore, to get reliable results, numerical models need to be validated for the same geometry and similar conditions.

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.

Performance Analysis of Elliptic-Profile Airfoil Cascade for Designing Reversible Axial Flow Fans

Because reversible fans must be able to provide similar performance in either rotation direction, they need to have completely symmetrical blades. In the present study, an elliptic profile with its maximum thickness of 8% chord length at the middle of the chord line is studied. For verification, the NACA 0012 airfoil was once analyzed two-dimensionally in the isolated formation and once in cascade formation with 0.55 and 0.83 solidities, and the obtained results were compared with numerical and experimental results. Three well-known Reynolds-averaged Navier–Stokes turbulence models including Spalart–Allmaras, realizable , and shear-stress transport were used to find the suitable turbulence method. After making sure of the accuracy of the modeling procedure, lift and drag coefficients were calculated for the elliptic profile for a wide range of velocities, solidities, and angles of attack. A number of issues not previously addressed in detail by previous works, such as the important stall phenomenon at low solidities, were solved, and the obtained aerodynamic coefficients were corrected by considering the occurrence of the stall. Finally, the method of using the colored cube for the design procedure of these blades was also proposed to reduce the gap between the design and the desired outcome.

Study on the Accuracy of RANS Modelling of the Turbulent Flow Developed in a Kaplan Turbine Operated at BEP. Part 1 - Velocity Field

This paper investigates the accuracy of Reynolds-averaged Navier-Stokes (RANS) turbulence modelling applied to complex industrial applications. In the context of the increasing instability of the e ...

Numerical analysis of the ROCOM boron dilution benchmark experiment using the CUPID code

Abstract The Rossendorf Coolant Mixing Model (ROCOM) boron dilution benchmark experiment was assessed using the CUPID code in the framework of a Coordinated Research Project by the International Atomic Energy Agency, namely, “Application of Computational Fluid Dynamics Codes for Nuclear Power Plant Design.” Two-equation Reynolds-Averaged Navier–Stokes (RANS) turbulence models, such as the standard k-e model, Re-Normalization Group (RNG) k-e model, and Shear Stress Transport (SST) k-ω model, were tested, and predictions of boron concentration were compared to measurements at the downcomer and core inlet in the reactor pressure vessel. The analysis result showed that the de-borated water slug injected from one cold leg was diffused by the turbulence mixing effect as it flowed downward in the downcomer and passes through a perforated drum in the lower plenum. The applied turbulence model affected the mixing patterns of the de-borated water, which resulted in a local distribution of boron concentration at the core inlet. This was the main concern of the boron dilution phenomena from the viewpoint of safety analysis. The result showed combining the CUPID code with the RANS turbulence models could reasonably predict the boron dilution phenomena in the reactor vessel when the proper y-plus wall treatment was assured, considering the characteristics of the turbulence models.

Validation of steady RANS modelling of isothermal plane turbulent impinging jets at moderate Reynolds numbers

Abstract The numerical modelling of impinging jet flows is not straightforward as it should not only solve the shear layer development in the free jet region, but also the near-wall behaviour (streamline curvature) and the resulting wall jets after impingement. This study presents a validation study of steady Reynolds-averaged Navier–Stokes turbulence models for predicting isothermal plane turbulent impinging jets at two different slot Reynolds numbers, i.e. Re = 8,000 (case I) and Re = 13,000 (case II), based on 2D particle image velocimetry measurements. In addition, an in-depth analysis of the results provided by the five different turbulence models: standard k − e (SKE), realisable k − e (RKE), RNG k − e , SST k − ω , and a Reynolds stress model (RSM), is performed. The results show that: (1) for both Reynolds numbers the best agreement with measured velocities and turbulent kinetic energy in the region near the jet nozzle is achieved with SST; (2) the best predictions of potential core length are provided by RNG (case I) and RKE (case II); (3) centreline distributions of velocities and turbulent kinetic energy are most accurately predicted by RNG and RKE for case I, while for case II the best agreement with experimental data is obtained by SKE and RNG; (4) the best overall performance for both cases in predicting velocities is provided by RKE, and by RKE and RNG when considering turbulent kinetic energy; (5) all models more accurately predict the jet spreading rate in the intermediate region than in the potential core region; (6) for both Reynolds numbers SKE provides the most accurate estimation of jet decay rate.

Numerical Analysis and Verification of the Gas Jet from Aircraft Engines Impacting a Jet Blast Deflector

The process of the gas jet from aircraft engines impacting a jet blast deflector is not only a complex fluid–solid coupling problem that is not easy to compute, but also a safety issue that seriously interferes with flight deck environment. The computational fluid dynamics (CFD) method is used to simulate numerically the impact effect of gas jet from aircraft engines on a jet blast deflector by using the Reynolds-averaged Navier-Stokes (RANS) equations and turbulence models. First of all, during the pre-processing of numerical computation, a sub-domains hybrid meshing scheme is adopted to reduce mesh number and improve mesh quality. Then, four different turbulence models including shear-stress transport (SST) k-w, standard k-w, standard k-ε and Reynolds stress model (RSM) are used to compare and verify the correctness of numerical methods for gas jet from a single aircraft engine. The predicted values are in good agreement with the experimental data, and the distribution and regularity of shock wave, velocity, pressure and temperature of a single aircraft engine are got. The results show that SST k-w turbulence model is more suitable for the numerical simulation of compressible viscous gas jet with high prediction accuracy. Finally, the impact effect of gas jet from two aircraft engines on a jet blast deflector is analyzed based on the above numerical method, not only the flow parameters of gas jet and the interaction regularity between gas jet and the jet blast deflector are got, but also the thermal shock properties and dynamic impact characteristics of gas jet impacting the jet blast deflector are got. So the dangerous activity area of crew and equipments on the flight deck can be predicted qualitatively and quantitatively. The proposed research explores out a correct numerical method for the fluid–solid interaction during the impact process of supersonic gas jet, which provides an effective technical support for design, thermal ablation and structural damage analysis of a new jet blast deflector.

Four equation k-omega based turbulence model with algebraic flux for supercritical flows

Hydrocarbon and nuclear fuels will contribute substantially to the growing global energy portfolio for some time to come. At the same time atmospheric carbon levels and economic concerns are increasingly shaping the power generation environment. Supercritical fluid technologies are being investigated to address both concerns. For example, direct fired supercritical CO2 power cycles offer key advantages for carbon capture and thermal efficiency. Additionally, the supercritical water reactor Generation IV nuclear reactor allows higher power densities and more efficient operation than current pressurized or boiling water reactors. As these technologies are developed, a need exists for accurate, yet cost-effective modeling and simulation solutions to assist with design and safety calculations. Supercritical fluid properties are strongly dependent on temperature which results in a number of unique flow features. Among these features are the complex buoyancy and buoyancy-turbulence interaction behaviors exhibited by supercritical flows that are not found in liquid or gas flows. Therefore, standard turbulence models with current model coefficient values are not likely to be applicable to supercritical fluid flows.The subject of this paper is efficient modeling and simulation of supercritical flows to support nascent technologies growing to maturation and operational deployment. We present a framework for developing Reynolds-Averaged Navier-Stokes turbulence models specifically equipped for the challenges of supercritical flows. A novel formulation of the algebraic heat flux model of the buoyancy production of turbulence term is used with a traditional shear stress transport model. To produce a new turbulence model for supercritical channel flows, the empirical coefficients of the resulting four equation model were calculated from data previously published by other authors regarding upward supercritical flow through heated pipes. The presented SST kt-ωt approach was validated against heated tube experiments to show predictive capabilities in moderate flow conditions, where buoyancy effects are important but not dominating of inertial effects.

Developing a framework for improvement of building thermal performance modeling under urban microclimate interactions

Coupled models developed from the building energy simulation (BES) and computational fluid dynamics (CFD) methods are occasionally used for analyzing the buildings thermal performance. Nevertheless, the large uncertainty in the input parameters of BES models and values of the closure coefficients of Reynolds-averaged Navier-Stokes (RANS) turbulence models restrict the accuracy of coupled BES-CFD models for thermal performance prediction in highly dense urban areas.Thus, a systematic framework for improving the accuracy of the coupled BES-CFD models is proposed in this study, consisting of an approximation technique and a stochastic optimization approach. In this framework, at first, a CFD model is improved with a closure coefficients optimization procedure using experimental data. In the second step, the improved CFD model is utilized to conduct a series of CFD simulations for real-geometry buildings in order to calibrate the BES model with the alteration of parameters such as the adaptive discharge coefficient, local wind profile, and convective heat transfer coefficients over the building façades.The developed framework is then applied to a small cross-ventilated office building surrounded by neighboring buildings. Deviations up to 60% are found in the prediction of the energy saving potential of cross-ventilation strategy by the default and calibrated BES models.

A review of computational fluid dynamics (CFD) simulations of the wind flow around buildings for urban wind energy exploitation

This article presents a review on computational fluid dynamics (CFD) applied to urban wind energy exploitation. The content comprises technical CFD aspects relevant for this application and the current state-of-the-art in building aerodynamics applied to urban wind energy. The majority of studies (more than 50% of the respective criteria) used Reynolds-averaged Navier-Stokes (RANS) turbulence models, the commercial solver ANSYS, simulated a full-scale geometry and studied an isolated building. For RANS, at least second order-accurate discretization schemes must be used, to improve turbulence kinetic energy prediction. In large-eddy simulation (LES) studies, a blending scheme is often needed to avoid numerical instability. Urban wind flow is very complex (i.e. detachment, stagnation), and rigorous validation and verification processes are needed, because only sophisticated turbulence models are able to yield acceptable results. The building-roof shape was optimized for the wind energy exploitation attending to both turbulence intensity and wind velocity. Conventional roof and roof edge shapes were studied, as well as the compatibility with the installation of solar panels. Wind turbines sitting was also discussed. Few simulations of wind turbines installed on building roofs were conducted using wind turbine models, whereas real geometries of vertical axis wind turbines were simulated and optimized.