Spanwise Resolution Research Articles

Mesh and model requirements for capturing deep-stall aerodynamics in low-Mach-number flows

The paper presents a comprehensive computational fluid dynamics investigation of the effects of grid resolution and turbulence-model choice for capturing the unsteady three-dimensional aerodynamic performance of NACA 0012 and 0021 airfoils, with specific focus on the deep-stall regime. At high angles of attack (α), wind turbine blades routinely experience vortex-induced vibrations, which can cause significant structural damages. Accurate predictions of post-stall aerodynamics can identify the frequencies at which such vibrations maybe triggered. In this context, the NACA 0012 airfoil simulations are conducted at a chord-based Reynolds number, , with the k-ω Shear-Stress Transport Reynolds-Averaged Navier-Stokes (RANS) and Improved Delayed Detached Eddy Simulation (IDDES) hybrid RANS-Large Eddy Simulation turbulence models. The effect of mesh resolution both in the wall-normal and spanwise directions is investigated. Only the IDDES model with a minimum spanwise resolution of 24 cells per chord length correctly predicts the aerodynamic forces. Spectral analysis shows the peak primary shedding frequency at , which signifies the end of the stall region. In the post-stall regime, both lift and drag frequencies drop asymptotically with increasing α. The Strouhal number, based on normalised chord length, remains nearly constant in this region. Based on this study, NACA 0021 airfoil runs are performed with IDDES for and on the finest wall-normal mesh and three spanwise grids. Simulations conducted on the finer spanwise grids demonstrate grid independence and show good agreement with experiments. The effect of varying on the airfoil frequency statistics is investigated. Additionally, comparison studies are presented to investigate the impact of airfoil thickness on the frequency content at . The results from the study provide guidance on the choice of mesh resolution with the IDDES model to accurately capture aerodynamic quantities for complex industrial applications.

Spanwise correlation and coherent structures of separated flow around rectangular 5:1 cylinder

Spanwise correlation and coherent structure of separated flow around a rectangular cylinder with a side ratio of B/D = 5 (B: breadth; D: depth of cylinder) are numerically investigated by Large Eddy Simulation (LES) at Reynolds number Re = 22,000. The investigation utilizes one series of three-dimensional simulations with various spanwise lengths up to 10D at a grid resolution of D/16 and another series of simulations with various spanwise grid resolutions as small as D/40 at a spanwise length of 5D, in addition to a two-dimensional simulation. The results show that a spanwise coherent flow structure with a wavelength of roughly 1.4D, associated with longitudinal vortices, exists in the separated flow. A spanwise length of 3D seems long enough to eliminate the influence of spanwise coherent flow structure on the global aerodynamic parameters and leads to convergent simulation results. The spanwise correlations of sectional forces and surface pressures decay with the spanwise distance. A finer spanwise resolution results in decreased spanwise correlations in the investigated spanwise resolution region. The results also imply that it is necessary to consider the combined effects of multiple interacting factors such as numerical method, three-dimensional grid discretization and turbulence model when selecting the spanwise resolution.

Aerodynamic and Acoustic Simulations of Thick Flatback Airfoils Employing High Order DES Methods

AbstractThe results of high fidelity aerodynamic and acoustic computations of thick flatback airfoils are reported in the present paper. The studies are conducted on a flatback airfoil having a relative thickness of 30% with the blunt trailing edge thickness of 10% relative to chord. Delayed Detached‐Eddy Simulation (DDES) approaches in combination with high order (5th) flux discretization WENO (Weighted Essentially Non‐Oscillatory) and Riemann solver are employed. Two variants of the DES length scale calculation methods are compared. The results are validated against experimental data with good accuracy. The studies provide guideline on the mesh and turbulence modeling selection for flatback airfoil simulations. The results indicate that the wake breakdown is strongly influenced by the spanwise resolution of the mesh, which directly contributes to the prediction accuracy especially for drag force and noise emission. The Reynolds normal stress and the Reynolds stress component have the largest contributions on the mixing process, while the contribution of the component is minimal. Proper orthogonal decomposition is further performed to gain deeper insights into the wake characteristics.

Large-eddy simulation of flow past a circular cylinder for Reynolds numbers 400 to 3900

The benchmarking case of flow past a circular cylinder at the Reynolds number (Re) of 3900 is computed with two open-source codes, OpenFOAM and Nektar++, which are based on the conventional finite volume method (FVM) and the high-order spectral/hp element method, respectively. By using the Nektar++ model, mesh convergence for the case Re = 3900 is demonstrated (perhaps for the first time) through a systematic mesh dependence study, which includes separate examinations of the spanwise domain length (Lz/D), spanwise resolution, and the resolution in the plane perpendicular to the spanwise direction. The computational efficiencies for the Nektar++ and OpenFOAM approaches are then compared. This benchmarking study adds value to the broad Nektar++ and OpenFOAM communities and to the numerical modeling of bluff-body flows in general. Based on the Nektar++ approach, the computations are then generalized to a range of Re = 400–3900. It is found that Lz/D = 3 is adequate for Re = 2500–3900, while an increased Lz/D = 6 is recommended for Re = 400–2000. Based on the present high-fidelity numerical data, the physical mechanisms for the variations in the wake recirculation length and the hydrodynamic forces and pressure on the cylinder with Re are explored. In particular, the physics behind the inverse correlation between the root mean square lift coefficient (CL′) and the wake recirculation length, which includes a significant decrease in CL′ over Re = 270–1500, is highlighted.

Spanwise resolution requirements for the simulation of high-Reynolds-number flows past a square cylinder

In the past, the coarse spanwise resolution was widely used for high-Reynolds-number flow simulations of a two-dimensional bluff body with the purpose of reducing the computational resources. The effects and requirements of spanwise resolution (dz/D, where D is the width of the cylinder) remain unclear for direct numerical simulation (DNS) or large-eddy simulation (LES). This numerical study, without any explicit subgrid-scale model, focuses on the typical flow around a square cylinder at the Reynolds number of 22,000. dz/D varies between 0.08 and 0.013. The requirement is recommended based on the systematical examination of aerodynamic pressure forces, vortex shedding in the wake, and flow structures in the separating shear layers. dz/D ≈ 0.04 is suggested sufficient for the prediction of mean and r.m.s aerodynamic pressures acting on the cylinder, mean and r.m.s velocity fields and small-scale turbulent motions in the wake. The coarser dz/D causes longer vortex formation length behind the cylinder and smaller fluctuating velocities around the cylinder (except the spanwise component). However, a stricter dz/D ≤ 0.02 is suggested necessary for accurately predicting the shear layer behaviors. Only if this requirement is satisfied, the subharmonic and harmonic of the Kelvin-Helmholtz instability can be captured, together with the process of laminar-turbulent transition in the shear layer. The shear layer when dz/D ≤ 0.02 is composed of interconnected small-scale spanwise and streamwise vortices. The shear layer has greater integrity along the spanwise direction and flaps as a whole at the same pace with vortex shedding. However, the shear-layer spanwise vortices are discrete when dz/D>0.02 as the streamwise vortices are not sufficiently reproduced.

Scale-resolving CFD modeling of a thick wind turbine airfoil with application of vortex generators: Validation and sensitivity analyses

Wind farms of Horizontal Axis Wind Turbines (HAWT) are increasing as number and size of single turbines and the blades with a degraded surface finish are studied as cause for decreasing of aerodynamic performance. Computational Fluid Dynamics (CFD) modeling of passive flow control devices like vortex generators is hence gaining importance to evaluate the increase in aerodynamic performance of degraded blades. This work is aimed at improving the state-of-the-art of RANS modeling of thick blades such as DU97-W-300 profile in clean configuration or equipped with VGs. The study is based on CFD scale-resolving methods (DES and SDES) to model the post-stall behavior at high Reynolds number. Furthermore, exhaustive sensitivity analyses are performed to assess the influence of time integration duration, grid span-wise resolution and domain width on the accuracy of the simulations. The results show that scale-resolving methods mark a significant step-ahead in stall simulation with respect to RANS models. Stall angle is captured with a better accuracy and the stall mechanism is reproduced in a more rigorous way. Final results present an average error of +11% on lift and −5% on drag coefficient for the clean profile and +1%/-10% respectively for the profile equipped with VGs.

Large-eddy simulations of flow past a square cylinder using structured and unstructured grids

The flow past a square cylinder at Re=2.2×104 is analyzed by large-eddy simulation (LES) using the fine grids in order to represent details of near-cylinder flows. The accuracy of LES on structured and unstructured grids is assessed from the engineering viewpoint, compared with previous studies. The finite differencing method code with 4th order central scheme for the convective term is used for structured LES, while the open-source finite volume method code (OpenFOAM 2.3.0) with 1st–2nd order schemes is applied for unstructured LES. Typical schemes in OpenFOAM are tested, i.e., “LUST” (blending of linear and linear upwind schemes), “limitedLinear” (TVD) and “linearUpwind” (linear upwind). In this study, three effects are emphasized: numerical schemes for convective terms, meshing strategies, and spanwise resolution and length. On the whole, OpenFOAM can obtain fairly accurate prediction of the time-averaged and r.m.s quantities no matter which numerical scheme is used. “LUST” and “linearUpwind” are suggested. Meshing refinement in wake can be a solution to improve the far-wake velocity distribution and to overcome the earlier energy decay of turbulent motions in the inertial subrange caused by artificial dissipation. Different degrees of instantaneous flow reattachment near the trailing edges are found in the results obtained by OpenFOAM. Flow reattachment is closely associated with the roll-up of shear layer, and the flow topology between the shear layer and the side wall featured by the frontal and leeward secondary vortex. In this regard, the refinement of hexahedra cells near cylinder gives a best solution among all present cases tested compared with the previous DNS result. Generally the Kelvin–Helmholtz instability can be accurately predicted by OpenFOAM under the present numerical conditions. In addition, the spanwise resolution seems no big effect in predicted results when less than 0.05D. By contrast, the increase in spanwise length to 14D from 4D plays an important role in obtaining reasonable spanwise correlation of pressure and consequently the overall fluctuating lifts.

Effect of mesh resolution on large eddy simulation of cloud cavitating flow around a three dimensional twisted hydrofoil

Unsteady cavitating turbulent flow around a twisted wing is simulated by using the large eddy simulation method. Two sets of grids with 10 million and 2 million nodes are used to investigate the influence of mesh resolution on the results. The results of non-cavitating flow with the coarse mesh agree well with the experiment, but the accuracy of the fine mesh results is remarkably higher for the cavitating flow, which indicates that more nodes are needed for the cavitating flow simulation than the non-cavitating flow. Then the parameters affecting the grid resolution are investigated. It is observed that the small size shedding vortex can only be captured by the fine mesh and the smaller grid spacing in the spanwise direction is needed to capture the details of re-entry jet. The re-entry jet in spanwise direction can affect the overall development of cavities, which is sensitive to the pressure gradient and spanwise resolution of the mesh.

Simulation and validation of a spatially evolving turbulent boundary layer up to [formula omitted

Results of a finely resolved large-eddy simulation (LES) of a spatially developing zero-pressure-gradient turbulent boundary layer up to a Reynolds number of Reθ=8300 are presented. The very long computational domain provides substantial assessment for suggested high Reynolds number (Re) trends. Statistics, integral quantities and spectral data are validated using high quality direct numerical simulation (DNS) ranging up to Reθ=4300 and hot-wire measurements covering the remaining Re-range. The mean velocity, turbulent fluctuations, skin friction, and shape factor show excellent agreement with the reference data. Through utilisation of filtered DNS, subtle differences between the LES and DNS could to a large extent be explained by the reduced spanwise resolution of the LES. Spectra and correlations for the streamwise velocity and the wall-shear stress evidence a clear scale-separation and a footprint of large outer scales on the near-wall small scales. While the inner peak decreases in importance and reduces to 4% of the total energy at the end of the domain, the energy of the outer peak scales in outer units. In the near-wall region a clear k-1 region emerges. Consideration of the two-dimensional spectra in time and spanwise space reveals that an outer time scale λt≈10δ99/U∞, with the boundary layer thickness δ99 and free-stream velocity U∞, is the correct scale throughout the boundary layer rather than the transformed streamwise wavelength multiplied by a (scale independent) convection velocity. Maps for the covariance of small scale energy and large scale motions exhibit a stronger linear Re dependence for the amplitude of the off-diagonal peak compared to the diagonal one, thereby indicating that the strength of the amplitude modulation can only qualitatively be assessed through the diagonal peak. In addition, the magnitude of the wall-pressure fluctuations confirms mixed scaling, and pressure spectra at the highest Re give a first indication of a −7/3 wave number dependence.

Numerical simulation of Görtler vortices in hypersonic compression ramps

A numerical study of the formation and evolution of Görtler type vortices over a compression ramp under an hypersonic flow is presented. Numerical predictions in laminar compression ramps (body/body-flaps configurations) usually require the inclusion of three-dimensional effects to correlate separation lengths with experimental measurements. Moreover, in the presence of large recirculation regions, the heat transfer calculated over the compression ramp severely underestimate experimental values. This discrepancy could be explained at least in part by the presence and effects of centrifugal disturbances. Indeed the regular striation patterns in heat transfer rates seen in experiments suggest this. In the present work numerical simulations were carried out over three-dimensional 15° compression ramps in a laminar hypersonic flow at Mach 6.85 and a Reynolds number per unit length of 2.45 × 10 6 m −1. The relatively high Görtler numbers obtained suggested that Görtler vortices might be important. In most cases, a spanwise periodic velocity perturbation is imposed on the flat plate ahead of separation. However for one case, which had a grid with a higher spanwise resolution, a regular striation pattern emerged without forcing. In this case, the pattern had a wavelength comparable to that found in experiments and as predicted from linear theory. A spanwise variation of 5–15% in the heat transfer close to the centreline was obtained in this case.

Detached Eddy Simulation of Flow around A-Airfoil

In this study the flow around the Aerospatiale A-airfoil at maximum lift (α = 13.3°) and Re = 2 × 106 is investigated by RANS and DES to quantify the influence of transient flow patterns on the quality of the flow prediction. This flow features a highly unsteady pressure-induced trailing-edge separation. The fairly high Reynolds number makes LES rather unattractive from a practical point of view as the numerical costs scale with ≈ Re1.95 [9] and lead to an unreasonable effort to carry out these simulations. Like LES, DES is designed to capture the unsteady flow features and consequently is supposed to give results superior to RANS. The RANS solution captures the separation, but is notable to predict transient vortex shedding. The application of DES to a 2D domain leads to results comparable to those obtained by 2D-RANS. Only the 3D-DES is capable of predicting both the unsteady flow features and the development of the boundary layer on the airfoil. As expected, the spanwise resolution has a strong impact on the vortex shedding and on the size of the separation bubble. Attention must be paid to both accommodating the full extent of the flow structures and providing the adequate spatial resolution in order to accomplish satisfactory results – that compare favourably with LES – at only a fraction of computational cost.

Direct numerical simulation of controlled transition in a flat-plate boundary layer

The three-dimensional development of controlled transition in a flat-plate boundary layer is investigated by direct numerical simulation (DNS) using the complete Navier-Stokes equations. The numerical investigations are based on the so-called spatial model, thus allowing realistic simulations of spatially developing transition phenomena as observed in laboratory experiments. For solving the Navier-Stokes equations, an efficient and accurate numerical method was developed employing fourth-order finite differences in the downstream and wall-normal directions and treating the spanwise direction pseudo-spectrally. The present paper focuses on direct simulations of the wind-tunnel experiments by Kachanovet al.(1984, 1985) of fundamental breakdown in controlled transition. The numerical results agreed very well with the experimental measurements up to the second spike stage, in spite of relatively coarse spanwise resolution. Detailed analysis of the numerical data allowed identification of the essential breakdown mechanisms. In particular, from our numerical data, we could identify the dominant shear layers and vortical structures that are associated with this breakdown process.