Three-dimensional Linear Eddy Modeling of a Turbulent Lifted Hydrogen Jet Flame in a Vitiated Co-flow

A new methodology for modeling and simulation of reactive flows is reported in which a 3D formulation of the Linear Eddy Model (LEM3D) is used as a post-processing tool for an initial RANS simulation. In this hybrid approach, LEM3D complements RANS with unsteadiness and small-scale resolution in a computationally efficient manner. To demonstrate the RANS-LEM3D model, the hybrid model is applied to a lifted turbulent N₂-diluted hydrogen jet flame in a vitiated co-flow of hot products from lean H₂/air combustion. In the present modeling approach, mean-flow information from RANS provides model input to LEM3D, which returns the scalar statistics needed for more accurate mixing and reaction calculations. Flame lift-off heights and flame structure are investigated in detail, along with other characteristics not available from RANS alone, such as the instantaneous and detailed species profiles and small-scale mixing.     

Modeling of Internal Reacting Flows and External Static Stall Flows Using RANS and PRNS

The reacting flow in a research lean direct injection (LDI) hydrogen combustor and the static stall of NACA0012 airfoil were simulated using both Reynolds averaged Navier–Stokes (RANS) and partially resolved numerical simulation (PRNS) approaches. The concept and the main features of the PRNS approach are briefly described. The PRNS basic equations are grid independent or grid invariant; the subscale models are a dynamic equation system. We consider PRNS as an engineering tool for the very large eddy simulation of complex turbulent flows. Two CFD codes, NCC and Wind-US, with two different subscale models (i.e. two- and one-transport equation models, respectively) are used in the presented PRNS simulations. Based on the comparisons with available experimental data, the numerical results indicate that the PRNS subscale models seem to be able to capture important large scale turbulent structures and to improve the quality of numerical simulations while keeping a relatively low cost comparable to the unsteady RANS simulations.     

Effects of Differential Diffusion on Predicted Autoignition Delay Times Inspired by H2/N2 Jet Flames in a Vitiated Coflow Using the Linear Eddy Model

Mixing and chemistry interactions in a H₂/N₂ jet flame into a vitiated coflow are considered key factors affecting autoignition. A 1-D numerical model under laminar flow condition first is simulated to reveal the effects of fuel species, pressure, and coflow properties on the autoignition with and without the consideration of preferential diffusion among species. Proper laminar reference autoignition delays are proposed and examined for different diffusion models. Next, the reference autoignition delays defined from laminar simulations are investigated in an example turbulent flow using the Linear Eddy Model (LEM). LEM is used to model the effect of turbulent mixing on autoignition, where we specifically investigate if the effect of turbulence on autoignition can be classified in two regimes, which are dependent on a proper reference laminar autoignition delay and turbulence time scale. The trend of the effect of differential diffusion on autoignition versus turbulence Reynolds is simulated and analyzed, and several tentative conclusions are drawn.     

Large Eddy Simulation of Scalar Mixing in a Coaxial Confined Jet

The highly turbulent flow occurring inside gas-turbine combustors requires accurate simulation of scalar mixing if CFD methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into an LES code, including assessment/testing of alternative discretisation schemes to avoid over/undershoots and excessive smoothing. Both second order accurate TVD and higher order accurate DRP schemes are assessed. The best performance is displayed by a DRP method, but this is only true on fine meshes; it produces similar (or larger) errors to a TVD scheme on coarser meshes, and the TVD approach has been retained for LES applications. The unsteady scalar mixing performance of the LES code is validated against published DNS data for a slightly heated channel flow. Excellent agreement between the current LES predictions and DNS data is obtained, for both velocity and scalar statistics. Finally, the developed methodology is applied to scalar transport in a confined co-axial jet mixing flow, for which experimental data are available. Agreement with statistically averaged fields for both velocity and scalar, is demonstrated to be very good, and a considerable improvement over the standard eddy viscosity RANS approach. Illustrations are presented of predicted time-resolved information e.g. time histories, and scalar pdf predictions. The LES results are shown, even using a simple Smagorinsky SGS model, to predict (correctly) lower values of the turbulent Prandtl number in the free shear regions of the flow, compared to higher values in the wall-affected regions. The ability to predict turbulent Prandtl number variations (rather than input these as in combustor RANS CFD models) is an important and promising feature of the LES approach for combustor flow simulation since it is known to be important in determining combustor exit temperature traverse.     

Modelling of thermal wall boundary conditions with temperature-dependent material properties for use in RANS

The present work extends a recently proposed P-function based model for describing the near-wall variation of temperature in forced convective turbulent flow to the case with temperature-dependent material properties. The extension essentially modifies the model formulations for describing the local variation of the turbulent mixing length and the turbulent Prandtl number. Direct Numerical Simulations (DNS) and experimental measurements are carried to provide comprehensive validation data for a wide range of Reynolds numbers, considering molecular Prandtl numbers well beyond unity. The observed good agreement of the predictions with the DNS data and experiments proves the present extended model as a well-suited approach for prescribing reliable thermal boundary conditions in Reynolds Averaged Navier-Stokes (RANS) simulations, assuming temperature-dependent material properties.     

Application of an Explicit Algebraic Reynolds Stress Model within a Hybrid LES–RANS Method

Large-eddy simulations (LES) still suffer from extremely large resources required for the resolution of the near-wall region, especially for high-Re flows. That is the main motivation for setting up hybrid LES–RANS methods. Meanwhile a variety of different hybrid concepts were proposed mostly relying on linear eddy-viscosity models. In the present study a hybrid approach based on an explicit algebraic Reynolds stress model (EARSM) is suggested. The model is applied in the RANS mode with the aim of accounting for the Reynolds stress anisotropy emerging especially in the near-wall region. For the implementation into a CFD code this anisotropy-resolving closure can be formally expressed in terms of a non-linear eddy-viscosity model (NLEVM). Its extra computational effort is small, still requiring solely the solution of one additional transport equation for the turbulent kinetic energy. In addition to this EARSM approach, a linear eddy-viscosity model (LEVM) is used in order to verify and emphasize the advantages of the non-linear model. In the present formulation the predefinition of RANS and LES regions is avoided and a gradual transition between both methods is assured. A dynamic interface criterion is suggested which relies on the modeled turbulent kinetic energy and the wall distance and thus automatically accounts for the characteristic properties of the flow. Furthermore, an enhanced version guaranteeing a sharp interface is proposed. The interface behavior is thoroughly investigated and it is shown how the method reacts on dynamic variations of the flow field. Both model variants, i.e. LEVM and EARSM, have been tested on the basis of the standard plane channel flow and even more detailed on the flow over a periodic arrangement of hills using fine and coarse grids.     

Numerical modeling of gravity currents in inclined channels

The mixing and wave formation processes in gravity currents induced by the rupture of a vertical dam initially separating a heavy and a light liquid are studied for different channel inclination angles. The calculations are performed using the LES and RANS models. It is shown that when the heavy liquid moves down the channel slope, the longitudinal and transverse internal waves break and form turbulent mixing zones. When the heavy liquid ascends the slope, the wavy motion mode predominates.     

Linear-Eddy Model Formulated Probability Density Function and Scalar Dissipation Rate Models for Premixed Combustion

A tabulated, pseudo-turbulent Probability Density Function (PDF) model for premixed combustion is proposed. The Linear-Eddy Model (LEM) is used to construct the PDFs for a temperature-based progress variable in a premixed, turbulent methane/air V-flame produced by the Cambridge slot burner. As a second case study, the LEM PDFs are similarly compared to PDFs extracted from Direct Numerical Simulations (DNS) of a turbulent premixed flame. LEM demonstrates the ability to reproduce the salient features from experimental and DNS PDFs; moreover, it is able to better capture turbulent effects than previously suggested laminar flamelet PDF models. The Scalar Dissipation Rate (SDR) for premixed combustion is likewise investigated. The stochastic nature of LEM enables it to mimic the overall behaviors of turbulent reactions inexpensively and qualitatively. Crucially, LEM appears to be well suited for the preprocessing tabulation of PDF and SDR models for a number of premixed combustion simulation strategies.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier–Stokes (RANS) computations are performed for water flow past an actuator disk model (representing a tidal turbine) placed in a rectangular channel of various blockages and aspect ratios. The study focuses on the effects of turbulent mixing behind the disk, as well as on the effects of channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.     

URANS Computations of Shock-Induced Oscillations Over 2D Rigid Airfoils: Influence of Test Section Geometry

The present article deals with recent numerical results from on-going research conducted at ONERA/DMAE regarding the validation of turbulence models for unsteady transonic flows, in which the mechanism of the shock-wave/boundary-layer interaction is important. The main goal is to predict the onset and extent of shock induced oscillations (SIO) that appear over the suction side of two-dimensional rigid airfoils and lead to the formation of unsteady separated areas. Computations are performed with the ONERA object-oriented software "elsA", using the URANS-type approach. In this approach, the unsteady mean turbulent flow is resolved using the standard Reynolds-averaged Navier–Stokes (RANS) equations and closure relationships involving standard transport equation-type models without any explicit modification due to unsteadiness. Applications are provided and discussed for two different test cases, one of which is rather well documented for CFD validation and described by mean-flow, phase-averaged and fluctuating data. Results demonstrate the importance of modelling the upper and lower walls of the test section when trying to capture SIO as precisely as possible with 2D computations, even though the adaptation of wind tunnel walls had been carefully considered. Finally, turbulence validation has been performed using one- and two-transport equation-type models, one of them resulting from in-house investigations for other turbulent flows applications.     

URANS prediction of flow fluctuations in rod bundle with split-type spacer grid

Turbulent flow in a rod bundle with split-type spacer grid has been studied using Unsteady Reynolds-Averaged Navier–Stokes (URANS) approach. In the previous studies of turbulent flow in rod bundles URANS (as well as steady-state RANS) simulations predicted mean velocity profiles fairly well. However, they severely underpredicted velocity fluctuations, which is investigated in the present study. Our simulations were performed with the Shear Stress Transport (SST) turbulence model and automatic wall-treatment using OpenFOAM, an open-source CFD code. Results of URANS simulations are compared with the measurements of the MATiS-H experiment, which was performed at Korean Atomic Energy Research Institute (KAERI) in 2011–2012.The URANS predictions of velocity fluctuations have been improved by appropriately summing up fluctuations resolved by the basic URANS model and non-resolved fluctuations, which were modelled with the turbulence model. This treatment of turbulent fluctuations, which are directly measured in high-quality experiments, allows more detailed evaluation of various URANS turbulence models. It was found out that the best agreement is achieved when resolved and modelled fluctuations are assumed to be uncorrelated, which indicates that the large-scale structures in this particular flow are distinct in the spectral space from the rest of turbulence. Turbulent flow in the MATiS-H experiment was reproduced by numerous authors using different approaches and our results are among the most accurate.     

Recent improvements in the Zonal Detached Eddy Simulation (ZDES) formulation

An efficient generalized Zonal Detached Eddy Simulation method (ZDES) is presented, which aims at performing hybrid Reynolds Averaged Numerical Simulation (RANS)/Large Eddy Simulation (LES) calculations for both internal and external aerodynamics problems. It is based on a zonal formulation of the hybrid length scale that allows to combine the zonal approach with the best features of Delayed Detached Eddy Simulation (DDES) (Spalart et?al. Theor Comput Fluid Dyn 20:181–195, 2006). In other words, the presumed weak point of a zonal approach, namely that the location of separation has to be known in advance, is now overcome. What is more, the problem of slow LES content development in mixing layers when they are treated neither in RANS nor in LES mode is investigated. It is argued that the subgrid length scale Δ_max?=?max(Δx, Δy, Δz) entering DDES is physically justified to shield the boundary layer but is definitely not a good subgrid length scale in LES mode. Remedies are proposed based on new zonal subgrid length scales that depend not only on the grid spacing but also on the flow solution and especially on the local vorticity vector. The method is validated on a spatially developing mixing layer as well as in a backward facing step flow and then applied to a three-element airfoil. It is argued in this latter case that a precise control of the RANS mode thanks to a zonal approach is essential. More generally, in all simulated cases in this study, ZDES has proven to be very efficient as regards the behavior in LES mode while retaining the strongest asset of DDES, namely the treatment of the attached boundary layer in RANS mode. The issue of zonal or non-zonal treatment of turbulent flows is also briefly discussed.     

The Relevance of a Back-Scatter Model for Depth-Averaged Flow Simulation

This study demonstrates the importance of a sophisticated sub-grid model when performing a depth-averaged unsteady RANS simulation of a shallow flow. The reduction of resolution and the spatial dimensions exclude important physical processes as present in three-dimensional turbulence. Especially the effect of the bottom turbulence on the formation of horizontal eddies appears of key importance. A method is proposed to incorporate these effects by means of a kinematic simulation that mimics the residual turbulent fluctuations in a straight channel flow after depth-averaging. This method is developed in the context of the evolution of large eddies in a shallow mixing layer. A comparison with experiments shows that the proposed method works satisfactory. Naturally, it does not fully account for the omission of all 3D-effects.     

Water entrainment due to spillway surface jets

Strong flow entrainment has been observed downstream of spillways constructed with flow deflectors. This water entrainment has important environmental and ecological impacts because it improves the mixing of powerhouse and spillway flows, but may negatively impact fish migration or create adverse flow conditions.

Most studies found in the literature attempt to explain this entrainment with turbulent mixing. Both reduced-scale hydraulic models and single-phase, isotropic RANS models grossly under-predict the degree of entrainment observed in prototypes. In this paper, an anisotropic model that accounts for the bubble volume fraction and attenuation of the normal velocity fluctuations at the free surface is presented. The model adequately predicts the main mechanisms causing water entrainment and compares well against experimental data for a round surface jet and for Brownlee Dam at model scale. It is shown that appropriate entrainment can only be captured if the turbulence anisotropy and the two-phase nature of the flow are modelled.     

Numerical study on supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder

Characteristics of supersonic mixing and combustion with hydrogen injection upstream of a cavity flameholder are investigated numerically using hybrid RANS/LES (Reynolds-Averaged Navier–Stokes/Large-Eddy Simulation) method. Two types of inflow boundary layer are considered. One is a laminar-like boundary layer with inflow thickness of $\delta_{\inf } = 0.0$ and the other is a turbulent boundary layer with inflow thickness of $\delta_{\inf } = 2.5\,{\text{mm}}$ . The hybrid RANS/LES method acts as a DES (Detached Eddy Simulation) model for the laminar-like inflow condition and a wall-modeled LES for the turbulent inflow condition where the recycling/rescaling method is adopted. Although the turbulent inflow seems to have just minor influences on the supersonic cavity flow without fuel injection, its effects on the mixing and combustion processes are great. It is found that the unsteady turbulent structures in upstream incoming boundary layer interact with the injection jet, resulting in fluctuations of the upstream recirculation region and bow shock, and induce quick dispersion of the hydrogen fuel jet, which enhances the mixing as well as subsequent combustion.     

Estimating turbulent-boundary-layer wall-pressure spectra from CFD RANS solutions

A stochastic model for the space–time turbulent boundary-layer wall-pressure spectrum is developed that uses statistical data from Reynolds-Averaged Navier–Stokes (RANS) solutions as input. The model integrates the source terms for the surface-pressure covariance across the boundary layer for user-specified space and time separations to form a discrete surface-pressure correlation function, the Fourier transform of which yields the surface-pressure wavenumber-frequency spectrum. By integrating RANS data into the model, it is able to respond to local geometry and flow conditions. Validation cases show that predicted surface-pressure power spectra respond appropriately to favorable, zero, and adverse pressure gradients. By operating as a post-processor of CFD RANS analyses, the model is a predictive tool that can be used in flow and flow-induced noise analyses. Because contemporary RANS models are able to predict flow statistics well for configurations of practical interest, this approach to modeling the turbulent boundary-layer forcing function is expected to generalize well to new flow configurations without requiring flow-specific tuning.