Aerodynamic noise simulation of the flow past an airfoil trailing-edge using a hybrid zonal RANS-LES

This paper document the evaluation of a zonal RANS-LES approach for the prediction of broadband and tonal noise generated by the flow past an airfoil trailing edge at a high Reynolds number. A multi-domain decomposition is considered, where the acoustic sources are resolved with a LES sub-domain embedded in the RANS domain. At the RANS-LES interface, a stochastic vortex method is used to generate synthetic turbulent perturbations. The simulations are performed with the general-purpose unstructured control-volume code FLUENT. The far-field noise is calculated using the aeroacoustic analogy of Ffowcs-Williams and Hawkings. The results of the simulation are compared with available acoustic and mean velocity measurements. The investigation demonstrates the ability of this approach to predict the aerodynamic and aeroacoustic properties of the flow. Two simulations are performed in order to address the sensitivity of the results to the perturbation model. The comparison clearly indicates the critical influence of the model.     

Near stall simulation of the flow around an airfoil using zonal RANS/LES coupling method

The objective of this current study is to investigate the course of events leading to stall just before its occurrence. The stall mechanisms are very sensitive to the transition that the boundary layer undergoes near the leading edge of the profile by a Laminar Separation Bubble (LSB). To provide helpful insights into this complex flow, different LES of the flow around an airfoil near stall have been achieved. Attention has been given to the transition mechanism in the LSB. In particular, the results are successfully compared to the linear stability theory. Furthermore, a zonal Reynolds averaged Navier-Stokes/large eddy simulation (RANS/LES) hybrid method has been employed for the same flow configuration to resolve more accurately the transitional flow than with the RANS approach. The analysis of the results highlights the strong impact of the LSB structure on the downstream boundary layer.     

Dynamic hybridization of MILES and RANS for predicting airfoil stall

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier-Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin-Lomax model with the Degani-Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA63₃-018, NACA63₁-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 10⁶. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.     

Zonal k-l based large eddy simulations

Zonal k-l based large eddy simulation (LES) approaches are presented. To reduce computational demands, near walls, Reynolds averaged Navier-Stokes (RANS) like modelling is used. The interface location for the differing models is either explicitly specified, or, based on length scale compatibility, allowed to naturally locate. With the latter approach the location is strongly grid controlled. When explicitly specified (based on turbulence physics grounds), to enhance results length scale smoothing is implemented. Using standard established LES and RANS model constants the zonal methods are shown to reproduce a satisfactory law of the wall. The approaches are implemented in both cell-vertex and cell-centred codes with similar results being found. Various other sensitivity studies are performed. These show that, as with standard LES, predictions are most sensitive to filter definition, first off wall grid node normal positions and temporal scheme order. For a non-isothermal periodic ribbed channel, the new zonal LES predictions are found to be significantly more accurate than those for an established RANS model and also LES.     

Advance in RANS-LES coupling,a review and an insight on the NLDE approach

Summary The aim of this article is twofold. The first purpose is to propose a review of existing RANS-LES methods and is addressed in the first part in a comprehensive way, detailing the advantages and the drawbacks of the different techniques. In a second time, a hybrid RANS-LES approach is presented, which can be interpreted as the most general case of the NLDE approach as defined by Morriset al. A decomposition into three parts of the exact solution of the Navier-Stokes equations is considered: mean flow, resolved fluctuations and unresolved (subgrid) fluctuations. The mean flow is computed using a classical RANS method, while resolved fluctuations are derived from a LES method. Several features on this approach are at first discussed in this paper, that are: the development of a non-zero mean for the resolved fluctuations (also called hereafter details), the computational problems due to the use of different schemes and meshes for the RANS and LES calculations, and the use of a boundary condition suited to the fluctuating part of the field. This approach is then used to simulate the acoustic sources of the flow around the slat of a high-lift system in landing configuration. The mean instabilities of the flow are studied and the resulting acoustic near field is carefully investigated.     

Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using near-wall modelling

We present a validation strategy for enhancement of an unstructured industrial finite-volume solver designed for steady RANS problems for large-eddy-type simulation with near-wall modelling of incompressible high Reynolds number flow. Different parts of the projection-based discretisation are investigated to ensure LES capability of the numerical method. Turbulence model parameters are calibrated by using a minimisation of least-squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow. Then the method is applied to the flow over a backward facing step at Re_h = 37,500. Of special interest is the role of the spatial and temporal discretisation error for low order schemes. For wall-bounded flows, present results confirm existing best practice guidelines for mesh design. For free-shear layers, a sensor to quantify the resolution quality of the LES based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at Re_h = 37,500.     

A Combined Large-Eddy Simulation and Time-Dependent RANS Capability for High-Speed Compressible Flows

An entirely new approach to the large-eddy simulation (LES) of high-speed compressible turbulent flows is presented. Subgrid scale stress models are proposed that are dimensionless functions of the computational mesh size times a Reynolds stress model. This allows a DNS to go continuously to an LES and then a Reynolds-averaged Navier–Stokes (RANS) computation as the mesh becomes successively more coarse or the Reynolds number becomes much larger. Here, the level of discretization is parameterized by the nondimensional ratio of the computational mesh size to the Kolmogorov length scale. The Reynolds stress model is based on a state-of-the-art two-equation model whose enhanced performance is documented in detail in a variety of benchmark flows. It contains many of the most recent advances in compressible turbulence modeling. Applications to the high-speed aerodynamic flows of technological importance are briefly discussed.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows

In this study we present a solution method for the compressible Navier-Stokes equations as well as the Reynolds-averaged Navier-Stokes equations (RANS) based on a discontinuous Galerkin (DG) space discretisation. For the turbulent computations we use the standard Wilcox k-ω or the Spalart-Allmaras model in order to close the RANS system. We currently apply either a local discontinuous Galerkin (LDG) or one of the Bassi-Rebay formulations (BR2) for the discretisation of second-order viscous terms. Both approaches (LDG and BR2) can be advanced explicitly as well as implicitly in time by classical integration methods. The boundary is approximated in a continously differentiable fashion by curved elements not to spoil the high-order of accuracy in the interior of the flow field.Computations are performed for the circular cylinder, the flat plate and classical airfoil sections like NACA0012. We compare our obtained results with experimental and computational data as well as analytical (boundary layer) predictions for the flat plate. The excellent parallelisation characteristics of the scheme are demonstrated, achieved by hiding communication latency behind computation.     

Numerical simulation of the transonic turbulent flow around a wedge-shaped body with a backward-facing step

A fully three-dimensional near-wall complex turbulent flow around a wedge-shaped body with a backward-facing step is considered with the transonic flow regime (Mach number M = 0.913) at the Reynolds number Re = 7.2 × 10⁶. The technology of the numerical simulation of problems of the class under study is represented in detail. A series of preliminary auxiliary calculations is carried out for choosing the optimal computational algorithm. The numerical results of the problem simulation based on the eddy-resolving hybrid RANS-LES approach IDDES are finally given for the full configuration. The validity of the results obtained is confirmed by comparing them to the corresponding experimental data.     

Efficient treatment of complex geometries for large eddy simulations of turbulent flows

Incompressible turbulent flow over a backward facing step at Re_h=5100 is investigated by large eddy simulations (LES). The ratio of the oncoming boundary layer thickness δ to the step height h was set to 1.2. Additionally channel flows at various Re_τ numbers are presented for the validation of the numerical code. The results are compared with existing DNS and experimental databases. The present study focuses on different procedures for LES of engineering problems in complex geometries using structured rectangular grids. Two different methods that are able to treat complex geometrical configurations are implemented, examined and compared; namely the domain decomposition approach based on Schur’s complement and the immersed boundary method. In the present study both methods make use of a fast direct Poisson’s pressure solver based on a heavily modified version of the public domain package FISHPAK. The latter was optimised and fully parallelised for shared memory architectures, for solutions on rectangular grids stretched in one or two directions. The resulting code reaches performances of 1.0 μs/node/iter, allowing low cost computations on grids of the order of million points. The main objective of the present study was to investigate the potential of different methods for LES in complex geometrical configurations like bluff body flows and wakes. One of the main findings is that careful selection of numerical methods and implementation techniques can lead to accurate and very efficient codes, where the geometric complexity does not lead to algorithmic or numerical complexity.     

Numerical and Physical Instabilities in Massively Parallel LES of Reacting Flows

LES of reacting flows is rapidly becoming mature and providing levels of precision which can not be reached with any RANS (Reynolds Averaged) technique. In addition to the multiple subgrid scale models required for such LES and to the questions raised by the required numerical accuracy of LES solvers, various issues related to the reliability, mesh independence and repetitivity of LES must still be addressed, especially when LES is used on massively parallel machines. This talk discusses some of these issues: (1) the existence of non physical waves (known as ‘wiggles’ by most LES practitioners) in LES, (2) the effects of mesh size on LES of reacting flows, (3) the growth of rounding errors in LES on massively parallel machines and more generally (4) the ability to qualify a LES code as ‘bug free’ and ‘accurate’. Examples range from academic cases (minimum non-reacting turbulent channel) to applied configurations (a sector of an helicopter combustion chamber).     

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

In this work, we combine (i) NURBS-based isogeometric analysis, (ii) residual-driven turbulence modeling and iii) weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows. While the first two ingredients were shown to be successful for turbulence computations at medium-to-high Reynolds number [I. Akkerman, Y. Bazilevs, V. M. Calo, T. J. R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. 41 (2008) 371–378; Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197 (2007) 173–201], it is the weak imposition of no-slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher Reynolds number [Y. Bazilevs, T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics, Comput. Fluids 36 (2007) 12–26; Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4853–4862]. These three ingredients form a basis of a possible practical strategy for computing engineering flows, somewhere between RANS and LES in complexity. We demonstrate this by solving two challenging incompressible turbulent benchmark problems: channel flow at friction-velocity Reynolds number 2003 and flow in a planar asymmetric diffuser. We observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data. This lends some credence to the proposed approach, which we believe may become a viable engineering tool.     

Implementation of synthetic turbulence inlet for turbomachinery LES

Large eddy simulation (LES) has the potential to model complex separated flows, where Reynolds Averaged Navier–Stokes (RANS) based methods often fail. An important aspect of LES is specifying correlated turbulent fluctuations at the inlet boundary. This is particularly important in turbomachines, where turbulence length scale and intensity play a key role in the correct prediction of component performance.In this work, a method is implemented into an unstructured Computational Fluid Dynamics (CFD) solver to impose correlated turbulent fluctuations in a compressible form. It is shown that compressibility effects are particularly important in turbomachinery and must be taken into account. The method uses a pre-processing method to generate a cube of isotropic, homogeneous turbulence. The velocity fluctuations so obtained are used to determine a fluctuating Mach number in order to evaluate the instantaneous total pressure and temperature fluctuations at domain inlet. In the authors knowledge this is one of the first attempts to define correlated fluctuations in a compressible form.The method is successfully applied to two turbomachinery related flows. Firstly, the jet flow from a propelling nozzle is investigated. Following this, the flow over a low pressure (LP) turbine blade is predicted. Results from the LES simulations show that modifications to the inlet conditions can significantly affect flow development. For the jet, changes in the shear layer and peak shear stress are shown, important in the context of high frequency sideline noise generated by the jet. Despite what is suggested in the literature the differences in shear stresses are important also in a non-swirling jet.For the LP turbine, incoming turbulent fluctuations modify the onset of transition and the extent of separation bubble. Without imposed turbulence fluctuations, loss is overpredicted by up to 50%. Moreover it is important to use a compressible solver. Despite the fact that the majority of the results proposed in literature on LP turbine is using incompressible solvers, the difference in terms of pressure coefficient, Cp, is comparable to turbulence contribution.     

Hybrid LES/RANS modelling of free surface flow through vegetation

Vegetated channels are environmentally friendly and frequently used to convey water for drainage and recreational purposes. The design and assessment of these channels often requires the use of numerical models which are based on the Reynolds Averaged Navier-Stokes (RANS) approach or Large Eddy Simulations (LES). It is well accepted that both approaches have their advantages and disadvantages. To overcome these disadvantages a hybrid model combining the RANS and LES methodologies is proposed in this work. The major task for the model development is to couple the RANS and the LES models effectively. Various methods have been investigated and the results are as follows. At the inflow boundary of the computational domain, a semi-analytical velocity profile for submerged vegetation is used as the RANS inflow condition to shorten the unrealistic flow transition region. At the interface of the upstream RANS region and the downstream LES region, turbulence fluctuations are artificially generated using a spectral line processor, with the mean velocity determined by using the frozen cloud assumption. At the interface of the upstream LES region and the downstream RANS region, a virtual momentum sink is imposed to dissipate the sub-grid scale fluctuations and to shorten the transition region. The final model has been verified against experiments of flow through submerged and emergent vegetation, as well as a partly vegetated channel.     

Flow over periodic hills - Numerical and experimental study in a wide range of Reynolds numbers

The paper presents a detailed analysis of the flow over smoothly contoured constrictions in a plane channel. This configuration represents a generic case of a flow separating from a curved surface with well-defined flow conditions which makes it especially suited as benchmark case for computing separated flows. The hills constrict the channel by about one third of its height and are spaced at a distance of 9 hill heights. This setup follows the investigation of Fröhlich et al. [Fröhlich J, Mellen CP, Rodi W, Temmerman L, Leschziner MA. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J Fluid Mech 2005;526:19-66] and complements it by numerical and experimental data over a wide range of Reynolds numbers. We present results predicted by direct numerical simulations (DNS) and highly resolved large-eddy simulations (LES) achieved by two completely independent codes. Furthermore, these numerical results are supported by new experimental data from PIV measurements. The configuration in the numerical study uses periodic boundary conditions in streamwise and spanwise direction. In the experimental setup periodicity is achieved by an array of 10 hills in streamwise direction and a large spanwise extent of the channel. The assumption of periodicity in the experiment is checked by the pressure drop between consecutive hill tops and PIV measurements. The focus of this study is twofold: (i) Numerical and experimental data are presented which can be referred to as reference data for this widely used standard test case. Physical peculiarities and new findings of the case under consideration are described and confirmed independently by different codes and experimental data. Mean velocity and pressure distributions, Reynolds stresses, anisotropy-invariant maps, and instantaneous quantities are shown. (ii) Extending previous studies the flow over periodic hills is investigated in the wide range of Reynolds numbers covering 100?Re?10,595. Starting at very low Re the evolution and existence of physical phenomena such as a tiny recirculation region at the hill crest are documented. The limit to steady laminar flow as well as the transition to a fully turbulent flow stage are presented. For 700?Re?10,595 turbulent statistics are analyzed in detail. Carefully, undertaken DNS and LES predictions as well as cross-checking between different numerical and experimental results build the framework for physical investigations on the flow behavior. New interesting features of the flow were found.     

Large-eddy simulation in a complex hill terrain enabled by a compact fractional step OpenFOAM® solver

We report computational fluid dynamics (CFD) code developments using the high-level programming syntax of the open source C++ library OpenFOAM®. CFD simulations utilizing the large-eddy simulation (LES) approach are carried out using the developed code in a real-world application. We investigate wind flowing over the Bolund hill, Denmark. In the present configuration a west–east wind meets the steep west side of the hill. Such conditions lead to flow separation at the location of a sharp cliff. A full scale simulation, with a simulation duration of over one month, is carried out on a supercomputer. Physically, about 45 min of real time is simulated in the LES enabling the statistical averaging of the results. The novelty of the paper consists of the following features: (1) we report validation results of the newly developed LES code for the Bolund hill case, (2) we show the high-level LES solver code in its entirety in a few tens of code lines which promotes transparency in CFD-code development in the OpenFOAM® environment, (3) the study is the first study to use LES in pointing out the complex 3d characteristics of the Bolund hill case with the computationally challenging west–east (270°) wind direction, and (4) based on the comparison with previous experimental data, and Reynolds averaged Navier–Stokes (RANS) simulations, the present LES gives so far the best match for the turbulent kinetic energy increase at the considered measurement positions.     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump

A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.