One-equation Eddy Viscosity Model Research Articles

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Quasi-dynamic subgrid-scale kinetic energy equation model for large-eddy simulation of compressible flows

A quasi-dynamic subgrid-scale (SGS) kinetic energy one-equation eddy-viscosity model is introduced in this paper for large-eddy simulation (LES) of compressible flows. With the additional SGS kinetic energy equation, the SGS kinetic energy can be predicted properly. Then, using the dual constraints of SGS kinetic energy and the SGS kinetic energy flux, the eddy-viscosity model can be determined exactly. Taking a similar scheme as the expansion of the SGS stress, other unclosed quantities in the equations to be solved could be well modelled separately. Therefore, with the advance of the equations, all the model coefficients can be determined dynamically. Differing from the classic dynamic procedure, the new methodology needs no test filtering, and thus it could also be called a quasi-dynamic procedure. Using direct numerical simulation of compressible turbulent channel flow, the$a$ $priori$test shows that the key modelled quantities of the suggested model display high correlations with the real values. In LES of compressible turbulent channel flows of the Mach number being$1.5$and 3.0, the proposed model can precisely predict some important quantities, including the mean velocity, Reynolds stress and turbulent flux, and it can also supply more abundant turbulent structures. For the compressible flat-plate boundary layer, the new model can correctly predict the transition process, mean velocity and turbulence intensities in the turbulent region. The results show that the proposed model has the advantage of scale adaptivity. Finally, the new model is applied to LES of turbulent mixing in spherical converging Richtmyer–Meshkov instability, and the accurate results show that the new model has a good ability for LES of complex fluids.

Turbulence Modeling for Leading-Edge Vortices: An Enhancement Based on Experimental Data

Low-aspect ratio wing planforms, such as delta wings, experience the predominance on their aerodynamic characteristics of large-scale leading-edge vortices separating around the leading edges. Due to their important application for highly maneuverable aircraft, the physical and aerodynamic understanding related to the vortex flow is of primary relevance. The investigation process is routinely performed with numerical simulations employing Reynolds-averaged Navier–Stokes equations. As the vortex grows in intensity, the limitation of ordinary models reduces the accuracy grade. Scale-resolving or more complex turbulence models can increase the accuracy, but the computational cost prohibits the application to a large envelope of cases. In the context of this work, the enhancement of a one-equation eddy-viscosity model is employed. The model is improved by formulating additional vortex source terms exclusively active inside the vortex-flow region and by employing a calibration procedure that is integrated into an iterative automated process where experimental data are used as targets for optimizing the model. The accuracy is enhanced for a cluster of cases around the calibration target, and it shows the potential of the application to large datasets that include several geometric and flow condition variations.

Subgrid-scale helicity equation model for large-eddy simulation of turbulent flows

A new one-equation eddy-viscosity model based on subgrid-scale (SGS) helicity is introduced in this paper for large-eddy simulation (LES) of turbulent flows. First, the governing equation of SGS helicity is deduced from the incompressible Navier–Stokes equations, and it reflects the transfer of the small-scale helicity that has been filtered out. We deduce a certain functional relation between the eddy viscosity and SGS helicity based on the kinetic energy and helicity spectra in the homogeneous and isotropic helical turbulence. For improving the accuracy, each unclosed term in the governing equation of SGS helicity is modeled independently, and the coefficients of these unclosed terms are constants or are determined dynamically. The new one-equation eddy-viscosity model is first tested and validated in the simulation of the homogeneous and isotropic helical turbulence. The a priori tests from the direct numerical simulation of forced homogeneous and isotropic turbulence show that the energy and helicity fluxes exhibit scale invariance in the inertial subrange. Additionally, the a posteriori tests demonstrate that the constant-coefficient and dynamic SGS helicity equation models can predict both the energy and helicity spectra more precisely than the common SGS models. For the LES of channel flow, the SGS helicity equation model can accurately predict the mean velocity, the turbulent stress, and the viscous shear stress and supply more abundant flow structures than the compared SGS model under the same grid resolution.

LES investigation of sheet-cloud cavitation around a 3-D twisted wing with a NACA 16012 hydrofoil

In this paper, we sought to investigate unsteady cavitating turbulent flows around a twisted three-dimensional NACA 16012 hydrofoil using the large eddy simulation (LES) and volume of fluid (VOF) methods. The one-equation eddy viscosity model (OEEVM) was used to calculate the sub-grid scale (SGS) stress tensor. The compressive velocity VOF technique and the Kunz cavitation model were also employed. Numerical simulation was performed using the interPhaseChangeFoam solver within the OpenFOAM framework. Cavitation simulation was performed at three cavitation numbers within the cloud cavitation regime; that is to say, cavitation numbers: 0.95, 1.15, and 1.35. Afterwards, the details of flow predictions including the pressure, velocity, streamlines, volume fraction of water phase, and turbulent kinetic energy were reported. Cavity behaviours, including growth, shedding, and collapse of the cavity, were considered in detail. Three-dimensional cavity structures such as primary and secondary shedding and the shedding of the U-shaped horseshoe vortex were reported as well. The present work illustrated the side-entrant jets and the radially diverging re-entrant jet corresponding to the three-dimensional effect of the twisted wing. The cavity pattern and the shedding cycle frequency agreed well with the available experimental observations.

Structural vibration of an elastically supported plate due to excitation of a turbulent boundary layer

High-Reynolds number turbulent boundary layers are an important source for noise and structural vibration. Indeed small features of a structure can have important influence on the resulting noise and vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic-finite-element solver for the structure. The flow solver is based on the OpenFOAM opensource CFD toolkit. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic finite element model with a suitable interpolation routine. A modal decomposition of the dynamic finite-element model is used to reduce the number of degrees-of-freedom of the numerical structural model. The numerical method is validated for the turbulent flow over a flat plate. The plate is elastically supported along its edges, and the turbulence is excited upstream ...

Anisotropic minimum-dissipation (AMD) subgrid-scale model implemented in OpenFOAM: Verification and assessment in single-phase and multi-phase flows

Minimum-dissipation sub-grid models represent simple alternatives to the Smagorinsky-type approaches to the implementation of sub-grid scales’ (SGS) effects in the large-eddy simulation (LES) approach. Recently, the anisotropic minimum-dissipation (AMD) model has been introduced, which is a static type of eddy-viscosity SGS model and is a new addition to this family. This model is easy to implement; furthermore, not only can it consider the effect of various directions in computing sub-grid stress, it can also operate transitional flows from laminar to turbulent. For the first time, we implemented AMD in the open source package OpenFOAM. Foremost, we verified the OpenFOAM implementation of the AMD model for the prediction of isotropic decaying turbulence, a temporal mixing layer and an internal channel flow. To achieve this, decaying turbulence was considered for the isotropic turbulence produced by a grid with a mesh size of 5.08 × 10–2 m in a flow of mean velocity of 10 m/s. The temporal mixing layer was simulated at a Reynolds number based on half the initial vorticity thickness of 105. Channel flow was investigated at the three frictional Reynolds numbers of 180, 395 and 590. The verification results revealed that the implemented AMD model in OpenFOAM offered satisfactory accuracy to capture decaying turbulence and temporal mixing layer and calculate boundary layer velocity profiles and first and second-order turbulent parameters in the channel flow on anisotropic grids. Following this, for the first time, we evaluated AMD's performance in predicting external non-cavitating and cavitating flows over a 3D sphere. Non-cavitating and cavitating flow over the sphere were considered at Re = 2 × 104 and Re = 1.5 × 106, respectively. The AMD results were then compared with the direct numerical simulation (DNS) data and the numerical results obtained from the established SGS models such as dynamic Smagorinsky (DS), one equation eddy viscosity model (OEEVM), detached eddy simulation (DES), and delayed detached eddy simulation (DDES), where applicable. In treating sphere flow, in spite of the use of a coarse grid rather than the alternative SGS models, the AMD model predicted accurate results for pressure coefficient, shear stress, and separation point location over the sphere as well as the velocity profile in the wake region. It was detected that the simulation time of the AMD model was lower than that of DS in all the considered test cases by approximately 10–16%.

Evaluation of Wray-Agarwal turbulence model for simulation of neutral and non-neutral atmospheric boundary layers

Wray-Agarwal (WA) turbulence model is a one-equation eddy-viscosity model derived from a blended k−ω/k−ε formulation. The model performance is better than the commonly used Spalart-Allmaras one-equation model and comparable to shear stress transport (SST) model, for a wide range of canonical flows in aerodynamics. This study proposes a Monin-Obukhov similarity theory (MOST) consistent modification of the buoyancy production/destruction term in this model to simulate the atmospheric boundary layer under different stratifications. The rough wall function is also modified to be consistent with MOST. A benchmark case for testing the streamwise homogeneity evaluated the model performance. In the tests, the wind and turbulence profiles did not decay along the stretch due to the model consistency with MOST. Adoption of the model for urban flow and wind energy simulations requires further testing.

Structural vibration of an elastically supported plate due to excitation of a turbulent boundary layer

High-Reynolds number turbulent boundary layers are an important source for noise and structural vibration. Indeed small features of a structure can have important influence on the resulting noise and vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic-finite-element solver for the structure. The flow solver is based on the OpenFOAM opensource CFD toolkit. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic finite element model with a suitable interpolation routine. A modal decomposition of the dynamic finite-element model is used to reduce the number of degrees-of-freedom of the numerical structural model. The numerical method is validated for the turbulent flow over a flat plate. The plate is elastically supported along its edges, and the turbulence is excited upstream ...

TCC-III Engine Benchmark for Large-Eddy Simulation of IC Engine Flows

A collaborative effort is described to benchmark the TCC-III engine, and to illustrate the application of this data for the evaluation of sub-grid scale models and valve simulation details on the fidelity of Large-Eddy Simulations (LES). The TCC-III is a spark ignition 4-stroke 2-valve engine with a flat head and piston and is equipped with a full quartz liner for maximum optical access that allows high-speed flow measurements with Particle Image Velocimetry (PIV); the TCC-III has new valve seats and a modified intake-system compared to previous configurations. This work is an extension of a previous study at an engine speed of 800 RPM and an intake manifold pressure (MAP) of 95 kPa, where a one-equation eddy viscosity LES model yielded accurate qualitative and quantitative predictions of ensemble averaged mean and RMS velocities during the intake and compression stroke. Here, experimental data were acquired with parametric variation of engine speed and intake manifold absolute pressure to assess the capability of LES models over a range of operating conditions of practical relevance. This paper focuses on the repeatability and accuracy of the measured PIV data, acquired at 1 300 RPM, at two different MAP (95 kPa and 40 kPa), and imaged at multiple data planes and crank angles. Two examples are provided, illustrating the application of this data to LES model development. In one example, the experimental data are used to distinguish between the efficacies of a one-equation eddy viscosity model versus a dynamic structure one-equation model for the sub-grid stresses. The second example addresses the effects of numerical intake-valve opening strategy and local mesh refinement in the valve curtain.

Partially Lagging One-Equation Turbulence Model

A partially lagging one-equation eddy viscosity model, based on the transformation of the turbulence closure through Bradshaw et al. (“Calculation of Boundary Layer Development Using the Turbulent Energy Equation,” Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593–616), is proposed. The model attempts to account for the turbulence history effects by spatially lagging the destruction/diffusion terms. The amount of relaxation is based on the von Kármán length scale. The present model does not assume equal diffusion coefficients of the and equations; therefore, third-order velocity gradients emerge. The performance of the present model is assessed against the Spalart–Allmaras model (“A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 1992-0439, 1992) and the one-equation model proposed by Menter (“Eddy Viscosity Transport Equations and Their Relation to the Model,” Journal of Fluids Engineering, Vol. 119, 1997, pp. 876–884), which is based on Bradshaw et al. (“Calculation of Boundary Layer Development Using the Turbulent Energy Equation,” Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593–616), and the assumption of equal diffusion coefficients. The behavior of the one-equation transformed model without the presence of third-order velocity gradients is also examined. The proposed model is validated through a comparison to a wide class of internal and external turbulent flows.

Computation of Flow in S Ducts with Wray–Agarwal One-Equation Turbulence Model

This paper focuses on the validation and application of a new one-equation eddy viscosity model derived from closure (the Wray–Agarwal model) for three-dimensional flows in serpentine diffusers (S ducts). The S-duct geometry produces streamline curvature and an adverse pressure gradient, resulting in flow separation. Two S-duct geometries are employed in this investigation: one was used in an experimental study conducted at NASA John H. Glenn Research Center in the early 1990s, and the other used in an experimental study conducted at ONERA–The French Aerospace Lab in 2006 and considered for computational fluid dynamics technology validation during the AIAA Propulsion Aerodynamics Workshops in 2012 and 2014. The computational fluid dynamics flow solver ANSYS Fluent is used for flow calculations. Results from the new “Wray–Agarwal” one-equation turbulence model, the widely used Spalart–Allmaras, and the shear-stress-transport models are compared to the available experimental data. Results obtained with the new Wray–Agarwal turbulence model are very promising. It is shown that this new model matches the experimental data better when compared to the Spalart–Allmaras and shear-stress-transport models.

Low-Reynolds-Number One-Equation Turbulence Model Based on Closure

Accurate turbulence modeling remains a critical problem in the prediction capability of computational fluid dynamics. In this paper, a new one-equation eddy-viscosity model is derived from closure. The equation used in this derivation includes a cross-diffusion term that allows the new model to switch between the model properties exhibited by the two-equation or turbulence models. In addition, the damping function used in conjunction with the proposed one-equation model has not been studied before in the literature. The new model is used to simulate several benchmark canonical flows involving both the free shear layer and wall-bounded turbulent flows with small separation regions. The open-source software OpenFOAM is used for the flowfield calculations. It is shown that the new model improves the accuracy of flow simulations compared to the widely used one-equation Spalart–Allmaras model and is competitive with the shear-stress-transport model.

RANS and Large Eddy Simulation of Internal Combustion Engine Flows—A Comparative Study

A comparative cold flow analysis between Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) cycle-averaged velocity and turbulence predictions is carried out for a single cylinder engine with a transparent combustion chamber (TCC) under motored conditions using high-speed particle image velocimetry (PIV) measurements as the reference data. Simulations are done using a commercial computationally fluid dynamics (CFD) code CONVERGE with the implementation of standard k-ε and RNG k-ε turbulent models for RANS and a one-equation eddy viscosity model for LES. The following aspects are analyzed in this study: The effects of computational domain geometry (with or without intake and exhaust plenums) on mean flow and turbulence predictions for both LES and RANS simulations. And comparison of LES versus RANS simulations in terms of their capability to predict mean flow and turbulence. Both RANS and LES full and partial geometry simulations are able to capture the overall mean flow trends qualitatively; but the intake jet structure, velocity magnitudes, turbulence magnitudes, and its distribution are more accurately predicted by LES full geometry simulations. The guideline therefore for CFD engineers is that RANS partial geometry simulations (computationally least expensive) with a RNG k-ε turbulent model and one cycle or more are good enough for capturing overall qualitative flow trends for the engineering applications. However, if one is interested in getting reasonably accurate estimates of velocity magnitudes, flow structures, turbulence magnitudes, and its distribution, they must resort to LES simulations. Furthermore, to get the most accurate turbulence distributions, one must consider running LES full geometry simulations.

Wind-field and pollution-dispersion simulation in a street canyon in Helsinki with ADREA-HF code

ADREA-HF, which is a Computational Fluid Dynamics (CFD) code, is utilised in order to
 numerically study the flow and concentration fields within a street-canyon area. The selected
 site is Runeberg Str., a typical urban street canyon with an aspect ratio of approximately 1:1
 in Helsinki, Finland. The ADREA-HF model is a transient, non-hydrostatic, dense transport
 code, especially developed for dispersion modelling of buoyant or passive gases over
 complex terrain in local scale. It solves the 3D unsteady Reynolds Averaged Navier-Stokes
 (RANS) equations treating complex multi-building domains with a porosity formulation. For
 modelling turbulence a one-equation eddy-viscosity model is used. The numerical results
 illustrate the flow and concentration fields within the canyon and also show the influence of
 the detailed geometry, such as, that of the street junction situated at the northern end of the
 canyon, and that of the boulevard at the southern end.

Modelling turbulence around and inside porous media based on the second moment closure

To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier–Stokes equations, there appear three unknown covariant terms in the momentum equation. They are namely the dispersive covariance, the macro-scale and the micro-scale Reynolds stresses, in the present study. For the macro-scale Reynolds stress, the TCL (two-component-limit) second moment closure is applied whereas the eddy viscosity models are applied to the other covariant terms: the Smagorinsky model and the one-equation eddy viscosity model, respectively for the dispersive covariance and the micro-scale Reynolds stress. The presently proposed model is evaluated in square rib array flows and porous wall channel flows with reasonable accuracy though further development is required.

Dynamic -equation model for large-eddy simulation of compressible flows

AbstractThis paper presents a dynamic one-equation eddy viscosity model for large-eddy simulation (LES) of compressible flows. The transport equation for subgrid-scale (SGS) kinetic energy is introduced to predict SGS kinetic energy. The exact SGS kinetic energy transport equation for compressible flows is derived formally. Each of the unclosed terms in the SGS kinetic energy equation is modelled separately and dynamically closed, instead of being grouped into production and dissipation terms, as in the Reynolds averaged Navier–Stokes equations. All of the SGS terms in the filtered total energy equation are found to reappear in the SGS kinetic energy equation. Therefore, these terms can be included in the total energy equation without adding extra computational cost.A prioritests using direct numerical simulation (DNS) of decaying isotropic turbulence show that, for a Smagorinsky-type eddy viscosity model, the correlation between the SGS stress and the model is comparable to that from the original model. Also, the suggested model for the pressure dilatation term in the SGS kinetic energy equation is found to have a high correlation with its actual value. Ina posterioritests, the proposed dynamic$k$-equation model is applied to decaying isotropic turbulence and normal shock–isotropic turbulence interaction, and yields good agreement with available experimental and DNS data. Compared with the results of the dynamic Smagorinsky model (DSM), the$k$-equation model predicts better energy spectra at high wavenumbers, similar kinetic energy decay and fluctuations of thermodynamic quantities for decaying isotropic turbulence. For shock–turbulence interaction, the$k$-equation model and the DSM predict similar evolutions of turbulent intensities across shocks, owing to the dominant effect of linear interaction. The proposed$k$-equation model is more robust in that local averaging over neighbouring control volumes is sufficient to regularize the dynamic procedure. The behaviour of pressure dilatation and dilatational dissipation is discussed through the budgets of the SGS kinetic energy equation, and the importance of the dilatational dissipation term is addressed.

Pulsed TV holography and schlieren studies, and large eddy simulations of a turbulent jet diffusion flame

In the search for an improved understanding of jet-flame dynamics we here compare predictions from large-eddy simulations (LES) and measurements using schlieren and holographic interferometry of a round turbulent jet diffusion flame. The studies concern a turbulent propane–air (C 3H 8–O 2/N 2) diffusion flame under ambient conditions at a Reynolds number of Re = 10 4 . The interferometric measurements were performed with an all-electronic method, pulsed TV holography, using a pulsed laser and a fast charge coupled device (CCD) camera. The LES calculations use the probability density function (PDF) flamelet approach with a beta function as the probability density function, whereas the subgrid turbulence is modeled with a one-equation eddy viscosity model. In order to validate the LES model quantitative comparisons of first-order statistical moments of the velocity were first made with available data for nonreactive jets. The LES model captures the statistics well. The next step in the validation process concerns comparing the jet-flame development between LES and the schlieren and pulsed TV holography data. To this end the results of the LES calculations were used to simulate instantaneous interference patterns using ray tracing. The LES model describes the overall behavior of the flame successfully.

Large Eddy Simulation of Combustion Instabilities in a Jet Engine Afterburner Model

Though turbulent reacting flows are often encountered in technical applications reliable prediction methods are lacking as a result of the complex nature of the physics. A promising approach to flows of practical interest is Large Eddy Simulation (LES). The philosophy behind LES is to explicitly simulate the large scales of the flow, directly affected by boundary conditions whilst modelling the smaller scales. The effects of the small unresolved scales appear as extra unknown terms in the LES equations that must be modelled. Subgrid models for reacting LES are more difficult to formulate than for non-reacting LES since also filtered reaction rates and other terms resulting from non-linear state equations need to be modelled. With the advent of transported PDF and linear-eddy models the situation has improved; due to the complexity and computational cost of similar models there is, however, still much to be gained from more conventional models. This study focuses on the development and application of a flame-wrinkling LES combustion model in which transport equations for a reaction coordinate, a modelled flame-wrinkling density and the laminar flame speed are derived, modelled and solved for. The unresolved transport terms in the momentum and energy equations are not particular to reacting flows and are modelled by a one-equation eddy-viscosity model. A centred second order accurate finite volume based scheme is used to solve the governing equations. The model is applied to a lean premixed propane air flame stabilised in the wake behind a triangular-shaped flameholder. Besides comparing with experimental data a discussion of different modes of combustion found to occur in this combustor is presented.