Open Source CFD Code Research Articles

Study on cross effect of mesh and turbulence model on separated flow prediction using a tandem cylinder case

Abstract Low dissipative separated flow prediction is still a great challenge in aeronautics engineering. An open-source CFD code named SU2 is employed to study the cross effect of mesh as well as turbulence model on the numerical resolution of separated flow for a tandem cylinder case. Firstly, a nonlinear variation of the numerical resolution for the separated flow is found by comparing the mean surface pressure distribution, mean streamwise velocity profile, the instantaneous vorticity magnitude as well as the aerodynamic forces on the rear cylinder. The resolution of separated flow from the medium mesh is the best compared to those getting from the coarse and fine mesh. Secondly, the reason causing the nonlinear variation of flow resolution is analyzed considering the influence of spatial discretization error and turbulent viscosity locally. A finer mesh would lead to a low spatial discretization error and then a high turbulent viscosity and then causes nonlinear variation of flow resolution. Finally, the existence of a “density boundary” of the mesh is proposed which could balance the spatial precision as well as turbulent viscosity and achieve the prediction of separated flow with a good resolution employing the RANS method.

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM + . For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed.The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. Given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

LES investigations of turbulent heat transfer structures with exponential power escalation

The BORAX-type accident is a key scenario in the safety design of pool-type experimental nuclear reactors. It considers a reactivity insertion large enough to initiate an exponential power escalation with a period as small as tens of milliseconds, necessitating effective heat removal by the coolant system. This study presents a computational analysis of single-phase transient heat transfer under thermal-hydraulic conditions relevant to such reactors, focusing on turbulent channel flow between planar fuel plates with highly subcooled water. Our investigation uses Large Eddy Simulation (LES) performed with TrioCFD, the open-source CFD code developed by the French Atomic Energy Commission (CEA). Several modeling options are tested: incompressible flow with temperature as a passive scalar, incompressible flow with varying viscosity, and quasicompressible flow with temperature-dependent viscosity and mass density. To evaluate the accuracy of our physical models, all simulations were performed under uniform conditions, using the same experimental parameters, mesh, and numerical strategies. The specific examined scenario involves a highly subcooled turbulent channel flow at moderate pressure, experiencing an exponential power increase. We ensure detailed turbulence resolution at the Batchelor scale in the wall normal direction close to the heating wall. This communication presents a comparative study of LES simulations of the single-phase flow under exponential power excursion at the wall. Subsequent analyses focused on the impact of different velocity-temperature couplings on the prediction of wall heat transfer, incorporating comparisons with experimental infrared thermometry measurements. Early in the transient phase, temperature peaks are confined within turbulent streaks, as reported in the existing literature. However, as the exponential power transient unfolds, the viscous layer and streak structures destabilize, leading to a more dispersed distribution of hot spots. Preliminary findings suggest a transition in heat transfer modes from turbulence-driven to conduction during the final stages of the single-phase transient.

Determination of transient heat transfer by cooling channel in high-pressure die casting using inverse method

Complex shapes of aluminum castings are typically manufactured during the short cycle process known as the high-pressure die casting (HPDC). High productivity is ensured by introducing die cooling through a system of channels, die inserts or jet coolers. Die cooling can also effectively help in reducing internal porosity in cast components. Accurate simulations based on sophisticated numerical models require accurate input data such as material properties, initial and boundary conditions. Although the heat is dominantly dissipated through die cooling, indicating the importance of knowing precise thermal boundary conditions, open literature lacks a detailed information about the spatial distribution of heat transfer coefficient. This study presents an inverse method to determine accurate heat transfer coefficients of a die insert based on temperature measurements in multiple points by 0.5 mm K-type thermocouples and a subsequent solution of the two-dimensional inverse heat conduction problem. The solver was built in the open-source CFD code OpenFOAM and the free library for nonlinear optimization NLopt. The results are presented for the commonly used 10 mm die insert with a hemispherical tip and coolant flow rates ranging from 100 l/h to 200 l/h. Heat transfer coefficients reach values well above 50 kW/m2K in the hemispherical tip, which is followed by a secondary peak and then a gradual drop to values around 1 kW/m2K further downstream.

Extension and Validation of the Turbomachinery Capabilities of SU2 Open Source Computational Fluid Dynamic Code

Abstract Computational Fluid Dynamic (CFD) tools have revolutionized the way to design engineering systems, but most established codes are proprietary and closed-source, making it difficult, if not impossible, to modify, debug, or add new features to the code. To provide a freely available open-source CFD code for turbomachinery aerodynamics and aeroelasticity, this paper enhances the turbomachinery capabilities of the open-source SU2 code and demonstrates its capabilities of single-passage steady simulation, full-annulus unsteady simulation, and aeroelasticity analysis in two high-speed compressors, namely NASA Stage 35 and TUDa-GLR-OpenStage, and a linear cascade SC1. For the single-passage steady simulation of NASA Stage 35, the SU2 results are validated against the measured data and verified against the commercial solver ansys cfx, and the performance characteristics results are in reasonably good agreement with each other. For the single-passage steady simulation of TUDa-GLR-OpenStage, grid and turbulence model sensitivity studies are performed and results are validated against the measured data, and SU2 can predict both the performance characteristics and the radial profiles with sufficient accuracy. For the full-annulus unsteady simulation of NASA Stage 35, it is demonstrated that SU2 can predict the propagation of inlet distortion equally well as ansys cfx. For the linear cascade, SU2 can predict the unsteady pressure and aerodynamic damping coefficient accurately. The presented results demonstrate the turbomachinery aerodynamics and aeroelasticity capabilities of SU2. The major modifications of SU2 made in this work will be shared with the code maintainer and the community in the future.

Effect of fluid elasticity and shear thinning on heat transfer from a heated sphere at moderate Reynolds numbers

The drag and heat transfer characteristics of an isothermal sphere in a FENE-P-type viscoelastic fluid have been studied in the steady axisymmetric flow regime. The governing equations, namely, mass, momentum, and energy equations, together with FENE-P type viscoelastic constitutive equations, have been solved using the finite volume method based opensource CFD code OpenFOAM over the following ranges of conditions: Reynolds number, 1 ≤ Re ≤ 100 ; Prandtl number, 1 ≤ Pr ≤ 50 ; Weissenberg number, 0 ​ ≤ Wi ≤ 10 and polymer extensibility parameter, 10 ≤ L 2 ≤ 500 for a fixed value of the polymer viscosity ratio of β = 0.5 . At low Reynolds numbers, fluid viscoelasticity causes an upward and downward shifting in the axial velocity profiles with reference to that in a Newtonian fluid along the upstream and downstream axis of the sphere, respectively. However, such a shift progressively diminishes with the increasing Reynolds number. Furthermore, a “velocity overshoot” and/or a “negative wake” is also observed in a viscoelastic polymer solution at low Reynolds numbers, and this is accentuated with the increasing Weissenberg number. The separation of boundary layers is seen to be suppressed with the increasing Weissenberg number. The drag coefficient decreases with the Reynolds number irrespective of the fluid type and the corresponding dependence on the Weissenberg number is found to be non-monotonic depending upon the values of Re and L 2. The average Nusselt number always increases with the increasing values of Re, Pr, and Wi and with the decreasing value of L 2. A limited number of simulations have also been carried out to show the effect of the temperature-dependent viscosity of the fluid on the flow dynamics and heat transfer characteristics. Finally, simple correlations for the drag coefficient and average Nusselt number are presented which not only capture the functional dependence but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.

On the use of flamelet model approach in analyzing the mixing-controlled spray flame dynamics

This research examines the application of unsteady flamelet modeling to consider the impact of turbulent-chemistry interaction (TCI) on a mixing-controlled spray flame. The model incorporates the Representative Interactive Flamelets (RIF) approach to represent the sub-grid scaled heterogeneous mixture along with chemical reactions. This is combined with an Eulerian Particle Flamelet Model (EPFM), which uses multiple flamelets to account for the history of unsteady flames. The results are compared with those of a first-order moment method known as the Well-Stirred Reactor (WSR) model. The numerical simulations were carried out using a Reynolds Averaged Navier–Stokes (RANS) solver incorporated in two different CFD platforms, a commercially available CFD code, CONVERGE, and C++ based open-source CFD code, OpenFOAM. The test conditions were employed based on the Engine Combustion Network (ECN) Spray-A setup. The simulation results obtained interchangeably using both CFD software are investigated to address essential aspects of the RIF model. In order to ensure accurate predictions in the mixing field, adjustments were made to the original OpenFOAM code to enhance the treatment of time-stepping for spray source terms. This refinement allows for an adequate resolution of spray-induced mixing. While there are slight variations in the implementation of the RIF model between OpenFOAM and CONVERGE, both CFD codes effectively reproduce the physics of mixing-controlled combustion. This includes accurately representing important phenomena like mixing-controlled turbulent spray flame and combustion recession.

CFD study of flameless combustion in a real industrial reheating furnace considering different H[formula omitted]/NG blends as fuel

On the path towards decarbonisation of the steel industry, the use of H2/NG blends in furnaces, where high temperatures are needed, is one of the alternatives that needs to be carefully studied. The present paper shows the CFD study carried out for a full-scale reheating furnace burner case. The real operating conditions as well as experimental measurements provided by the furnace operator were used to validate the results and reduce simulation uncertainties. The burner under consideration (2.5 MW) works in flameless mode with natural gas and preheated air (813 K). Starting from this point, another three fuel blends with volumetric percentages of 23% (also known as G222), 50% and 75% of H2 in natural gas were considered. For this purpose, the open source CFD code OpenFOAM was used, where the novel NE-EDC turbulence-chemistry interaction model was implemented, which has already been successfully validated specifically for flameless combustion in a furnace. The implementation incorporated an enhanced approach for calculating the chemical time-scale, coupled with a specific post-processing solver to predict NOx emissions. The study analyses the relative impact of the considered fuel blends on NOx formation and flameless regime. The modelling results demonstrated the burner’s capability to operate efficiently with high concentrations of hydrogen, maintaining flameless regime in all cases. This condition ensured uniform temperature distributions and low levels of NOx emissions, reaching a maximum value of 86 mg/m3. These results indicated the proper functionality of the existing natural gas-based burner with H2/NG blends, which was the primary requirement for the conversion process.

Analyses of International Standard Problem ISP-47 TOSQAN experiment with containmentFOAM

The ISP-47 TOSQAN experiment was analyzed with containmentFOAM which is an open-source CFD code based on OpenFOAM. The containment phenomena taking place during the experiment are gas mixing, stratification and wall condensation in a mixture composed of steam and non-condensable gas. The k-ω SST turbulence model was adopted with buoyancy turbulence models. The wall condensation model used is based on the diffusion layer approach. We have simulated the full TOSQAN experiment which had a duration 20000 s. Sensitivity studies were conducted for the buoyancy turbulence models with SGDH and GGDH and there were not significant differences. All the main features of the experiments namely pressure history, temperature, velocity and gas species evolution were well predicted by containemntFOAM. The simulation results confirmed the formation of two large flow stream circulations and a mixing zone resulting by the combined effects of the condensation flow and natural convection flow. It was found that the natural convection in lower region of the vessel devotes to maintain two large circulations and to be varied the height of the mixing zone as result of sensitivity analysis of non-condensing wall temperature. The computational results obtained with the 2D mesh grid approach were comparable to the experimental results.

Interaction of two cylinders immersed in a viscous fluid. On the effect of moderate Keulegan–Carpenter numbers on the fluid forces

This work deals with the hydrodynamic interaction of two parallel circular cylinders, with identical radii, immersed in a viscous fluid initially at rest. One cylinder is stationary while the other one is imposed a harmonic motion with a moderate amplitude of vibration. The direction of motion is parallel to the line joining the centers of the two cylinders. The two dimensional fluid–structure problem is numerically solved by the Arbitrary Lagrangian–Eulerian method implemented in the open-source CFD code TrioCFD. First, we show that the fluid forces on the two cylinders are aligned with the direction of the imposed motion. Second, we show that the moderate oscillations of the moving cylinder create nonlinear effects in the fluid that strongly affect the characteristics (Fourier harmonics) of the hydrodynamic force acting on the stationary cylinder. The fluid force on the moving cylinder is shown to be poorly affected by the nonlinear effects, which makes it possible to extend the linear concept of self-added mass and damping coefficients. First, we show that the self-added coefficients decrease as Sk−1/2, with Sk the Stokes number (dimensionless number constructed from the imposed vibration frequency). Second, we show that the self-added mass (resp. damping) decreases (resp. increases) as −KC3 (resp. +KC3), with KC the Keulegan–Carpenter number (ratio between the imposed amplitude vibration and the separation distance between the cylinders). These variations are included in new power laws derived from nonlinear regressions of the numerical results. These new power laws for the self-added coefficients combine the effect of both Sk and KC, covering the viscous (Sk≥500) and weakly nonlinear (KC≤0.3) regimes.

Spray Flamelet Modeling of Turbulent Two-Phase Reacting Flows with Multi-Component Fuel in a Lean Direct Injection Combustor

ABSTRACT Towards the numerical evaluation of the performance in aero-engine combustors, implementing detailed reaction kinetics into the large eddy simulation (LES) cost-effectively is highly desirable. In this work, a newly-developed spray flamelet model is combined with a four-component jet fuel surrogate model to allow integration of the detailed kinetics in the open-source CFD code. The spray flamelet approach (SFGM) can take into account the non-adiabatic effect caused by the evaporating spray and can directly reflect the preferential evaporation, as well as multiple combustion regimes present in complex spray combustion systems. The coupling of the SFGM-LES approach is assessed by comparison with the experimental data from a Lean Direct Injection (LDI) combustor, where the real aviation kerosene, Jet-A, was utilized. The SFGM-LES approach well predicts the experimental statistics in both gas and liquid phases. It is capable of capturing the rich physics and complex flame structures, including the preferential evaporation effect and the multi-regime combustion phenomenon. The present work demonstrates that the complex nature of multi-components and the multiple-combustion regimes in the two-phase combustion can be directly included in the spray flamelet approach, and thus this model can provide new insights into the turbulent spray combustion phenomena.

멀티 블록 격자 재분할이 자동차 공기역학에 미치는 영향

The impact of multi-block mesh refinement on automobile aerodynamics was investigated using three refinement methods: (1) overall mesh refinement, (2) ground mesh refinement, and (3) prism layer control. The open source CFD code, OpenFOAM V10, was utilized and simulations were conducted on the full-scale Notchback DrivAer model. For each method, the effects of mesh refinement were analyzed by refining different regions. In the overall mesh refinement study, successive multi-block grid refinement regions were established - the grid size becomes finer as the block is closer to the car surface. The lift coefficient was affected by grid refinement in regions near the automobile body. The ground mesh refinement study was conducted by controlling two grid sizes related to the ground region: volume mesh and surface mesh. The prediction of drag coefficient was fairly robust with ground region refinement, and the lift coefficient was more accurate with a smaller ground region grid. However, an excessively small surface grid reduced the accuracy of both drag and lift coefficients. In the prism layer study, the accuracy of the drag coefficient was independent of the prism layer setup, while the layer thickness and expansion ratio had a significant impact on the lift coefficient.

KIT Multi-scale thermal–hydraulic coupling methods for improved simulation of nuclear power plants

In a Nuclear Power Plant (NPP), the Thermal-Hydraulic (TH) phenomena take place at different scales in the core and the primary and secondary circuits. Thus different TH codes have been developed to describe the phenomena at the macro- and meso- scale (system, sub-channel, porous media codes). Besides, the use of general-purpose CFD codes for the analysis of specific local problems is rapidly increasing. To take full advantage of the code's strength, the multi-scale TH approach which couple those codes together is becoming a trend in recent years. At Karlsruhe Institute of Technology (KIT), those multi-scale TH approaches involve the system, sub-channel, and CFD codes: 1) the system code TRACE and the sub-channel code SubChanFlow (SCF) were coupled to improve the prediction of the core thermal hydraulics; 2) the system code TRACE and the open-source CFD code TrioCFD were also coupled to improve the prediction of the TH phenomena inside the Reactor Pressure Vessel (RPV). Those works are based on an Interface for Code Coupling (ICoCo) either with or without the SALOME platform. The current investigations demonstrate the potential of multi-scale TH coupling approaches for improved safety-related analysis of the NPP behavior under accidental conditions. In the future, the focus of KIT work is on multiscale coupling based on domain decomposition using both ICoCo and user define functions of commercial CFD codes.

Development and Validation of an Open Source CFD Code for Analysis of Aerospace Vehicles

Development and Validation of an Open Source CFD Code for Analysis of Aerospace Vehicles

Wind Resource Assessment in Building Environment: Benchmarking of Numerical Approaches and Validation with Wind Tunnel Data

In the framework of the wind energy network for distributed generation in urban environments for most South American countries, wind resource assessment studies have been carried out in activities to establish a suitable methodology to assess the wind potential in urban environments. Some methodologies are already published in research studies, and the wind tunnel is the most accurate solution to obtain insight into the wind resource when measurements are unavailable, which is the most frequent case. Nevertheless, besides its validity, one cannot disregard the high cost of producing a scaled urban model and access to a wind tunnel. In this sense, this paper compares results from a wind tunnel experiment and different numerical modeling approaches. Two commercial models (WindSim and Wasp Engineering) and one open-source CFD code (OpenFOAM) are used. The results from the modeling simulation concluded that CFD models could achieve lower deviations for the mean wind speed and turbulence intensity when compared with non-CFD models. With such results, CFD modeling is a promising tool for reliably evaluating wind potential in urban environments.

Computational assessment of biomass dust explosions in the 20L sphere

Determination of the explosion severity parameters of biomass is crucial for the safety management and dust explosion risk assessment of biomass-processing industries. These are commonly determined following experimental tests in the 20L sphere according to the international standards. Recently, CFD simulations have emerged as a reliable alternative to predict the explosion behavior with good accuracy and reduced labor and capital. In this work, numerical simulations of biomass dust explosions are conducted with the open-source CFD code OpenFOAM. The multi-phase (gas-solid) flow is treated in an Eulerian-Lagrangian framework, using a two-way coupling regime and considering the reactions of biomass conversion (moisture evaporation, devolatilization, and char oxidation), the combustion of volatile gases, and convective and radiative heat transfer. The model is validated with pressure-time and concentration-dependent experimental measurements of two biomass samples. Results suggest that the characteristics of the cold-flow (ı.e., turbulence levels, actual dust concentration, spatial distribution of the dust cloud, and turbophoresis effect) govern the course of the explosion process, and depend strongly on particle size, dust concentration, and ignition delay time effects. These findings may be relevant in the design of better dust explosion testing devices and to the reexamination of the guidelines for the operation of the experiment. Finally, a thorough discussion on the explosion pressures, degree of biomass conversion, flame temperature, flame propagation patterns, and the dust agglomeration effect is presented.

Numerical investigations on flashback dynamics of premixed methane-hydrogen-air laminar flames

Injecting hydrogen into the natural gas network to reduce CO2 emissions in the EU residential sector is considered a critical element of the zero CO2 emissions target for 2050. Burning natural gas and hydrogen mixtures has potential risks, the main one being the flame flashback phenomenon that could occur in home appliances using premixed laminar burners. In the present study, two-dimensional transient computations of laminar CH4 + air and CH4 + H2 + air flames are performed with the open-source CFD code OpenFOAM. A finite rate chemistry based solver is used to compute reaction rates and the laminar reacting flow. Starting from a flame stabilized at the rim of a cylindrical tube burner, the inlet bulk velocity of the premixture is gradually reduced to observe flashback. The results of the present work concern the effects of wall temperature and hydrogen addition on the flashback propensity of laminar premixed methane-hydrogen-air flames. Complete sequences of flame dynamics with gradual increases of premixture velocity are investigated. At the flame flashback velocities, strong oscillations at the flame leading edge emerge, causing broken flame symmetry and finally flame flashback. The numerical results reveal that flashback tendency increase with increasing wall temperature and hydrogen addition rate.

An open-source workflow for open-cell foams modelling: Geometry generation and CFD simulations for momentum and mass transport

• We developed an open-source workflow to characterize open-cell solid foams. • The geometry generation is performed by using the computer graphics code Blender. • Fluid flow and mass transfer are simulated using open-source CFD code OpenFOAM. • From the CFD results permeability and filtration rate are calculated. • The workflow (available online) is used to investigate a large number of different foams. Open-cell foams are porous materials characterized by high porosity and large specific surface, industrially employed as catalyst supports or particulate filters. These materials can be modelled using periodic lattices, or with more complex approaches based on Voronoi tessellations. This work introduces, tests, and makes available an open-source workflow ( Agostini, 2021 ) based on Blender that can reproduce great varieties of geometries with a limited cost for their modeling. An example of the exploration capabilities of this workflow is presented in the form of CFD simulations for flow field and mass transfer (performed with OpenFOAM) on the created geometries, eventually obtaining an effective particle deposition/filtration coefficient K d . The results are interpreted using constitutive equations and other functional forms depending on geometric parameters which prove to be insufficient in explaining the variations in filtration performance, highlighting the need for more detailed exploration, the objective for which this workflow was developed.

OpenFOAM CFD simulation of critical heat flux in vertical pipe under typically PWR conditions

This paper aims to see how well the open-source CFD code OpenFOAM can simulate the critical heat flux (CHF) in vertical pipe under extreme conditions, close to PWR operating conditions. The two-fluid approach combined with an extended wall boiling model was used to forecast CHF. The 2006 CHF look-up table was employed as benchmark data. The wall temperature jump was used as the criterion for predicting departure from nucleate boiling (DNB) type CHF. Good agreement was obtained between CHF from look-up table and calculated values. The effects of pressures, mass flow rates, and equilibrium qualities on CHF are investigated. CHF location and maximum volume fraction at corresponding CHF were also obtained. Most of the deviations are within 15% of error. The average absolute error of the simulated CHF was 7%. The findings indicate that OpenFOAM promises to forecast boiling flow and CHF in the PWR reactor fuel assembly geometry.

A rational hybrid RANS-LES model for CFD predictions of microclimate and environmental quality in real urban structures

We report on the application and comparative assessment of two rational turbulence modelling approaches for the computer simulation of air flow and pollutant dispersion in real urban environment: a stand-alone unsteady Reynolds-averaged Navier-Stokes eddy-viscosity model (URANS), and its blend with Large-eddy simulations (LES) in a hybrid mode (HRL). The elliptic-relaxation (k−ε)ζ−feddy-viscosity model was applied in both methods. The models, verified earlier in a range of engineering flows including heat transfer, were here validated in two environmental benchmark cases, a single building and an idealized urban settlement, both subjected to a steady wind. The velocity field and pollutant concentration are better predicted by the HRL method in both benchmarks. The HRL is then applied to predictions of air flow and spreading of pollutant from road traffic in downtown of a real city (Sarajevo) containing 100 realistic buildings. The simulations were performed with the in-house open-source CFD code T-Flows, specifically optimized for a fast and efficient high-quality unstructured meshing of the terrain orography and building configurations. The benchmark validations demonstrated that, compared with the standard k−ε, in typical urban applications with complex urban shapes and arrangements the accuracy and credibility of the predictions can substantially be improved by applying a physically sounder and yet still relatively simple ζ−f eddy-viscosity model that specifically accounts for the elliptic inviscid wall-blocking effects and near-wall stress anisotropy. The benchmarking also showed that still further improvements are achieved by using the HRL scheme which ensures a rational balance in capturing the important physics and the computational economy.