Delayed detached-eddy simulations of NACA wing sections using spectral elements

Turbulent flow at Reynolds numbers 5 · 104 to 106 around the NREL S826 airfoil used for wind turbine blades is simulated using delayed detached eddy simulation (DDES). The 3D domain is built as a replica of the low speed wind tunnel at the Norwegian University of Science and Technology (NTNU) with the wind tunnel walls considered as slip walls. The subgrid turbulent kinetic energy is used to model the sub-grid scale in the large eddy simulation (LES) part of DDES. Different Reynoldsaveraged Navier-Stokes (RANS) models are tested in ANSYS Fluent. The realizable k - ∈ model as the RANS model in DDES is found to yield the best agreement of simulated pressure distributions with the experimental data both from NTNU and the Technical University of Denmark (DTU), the latter for a shorter spanwise domain. The present DDES results are in excellent agreement with LES results from DTU. Since DDES requires much fewer cells in the RANS region near the wing surface than LES, DDES is computationally much more efficient than LES. Whereas DDES is able to predict lift and drag in close agreement with experiment up to stall, pure 2D RANS simulations fail near stall. After testing different numerical settings, time step sizes and grids for DDES, a Reynolds number study is conducted. Near stall, separated flow structures, so-called stall cells, are observed in the DDES results.

Numerical Simulation of Unsteady Separated Flow over a Delta Wing Using Cartesian Grids and DES/DDES

The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using Delayed Detached Eddy Simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark LES. The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier-Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved Large Eddy Simulations (LES). Additionally, the results of the transitional DDES model are compared to DDES without a transition model, RANS eddy viscosity model and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, transition process and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

Small-scale side-channel or regenerative blowers are used in various applications, e.g. as components in medical system solutions, for air-circulation in space suits or as hydrogen recirculation blowers in PEM fuel cells. These non-conventional turbomachines are characterized by high energy transfer rates, generating large pressure differentials at low volumetric flow rates and low flow pulsations. They are simple in construction, reliable and require little maintenance. Typical drawbacks of these machines are their low aerodynamic efficiencies and unfavorable sound radiation. The present study examines the performance of a small-scale side-channel blower with semi-circular side-channel and rotor cross-sections (in the meridional plane) as function of impeller design, i.e., blade angle and inner-to-outer radius ratio, for different rotational speeds. Head/flow performance curves are determined via experiments and selected machine designs are further evaluated by means of numerical simulation using the commercial CFD solver ANSYS Fluent v. 2022 R1. Unsteady simulations are carried out using the transient sliding mesh method and predictions from different turbulence models, i.e., RSM (Reynolds stress model), DDES (Delayed Detached-Eddy Simulation) and k-ω SST turbulence model, are evaluated for selected machine configurations. While the RSM and DDES models capture smaller vortical structures relevant for accurate predictions of acoustic behavior, mean meridional velocities are overestimated by these models, thereby overpredicting the pressure rise in comparison to the experiments. In contrast, the k-ω SST model is found to only slightly overpredict the pressure rise across the machine.

Accurate prediction of high Reynolds number flow fields around complex geometries requires turbulence models that have favorable characteristics with regard to numerical stability, computational cost, mesh sensitivity, and accuracy. In order to investigate the feasibility of a new Hybrid RANS/LES (HRL) model with respect to these characteristics, numerical simulations were performed over a rearward facing step at ReH = 37,000 and around a GLC-305 airfoil configured with a 22.5-minute glaze ice accretion at Re = 3.5x10 6 , M = 0.12, and α = 6°. In the case of rearward facing step flow, comparisons were made between simulation results that employed a RANS model (Shear Stress Transport (SST)), the Delayed Detached Eddy Simulation (DDES) model, and the new HRL model. Mean velocity profiles of the new HRL model predictions showed better agreement with experimental data, in comparison with RANS and DDES model predictions. Both RANS and the new HRL model predictions of the turbulent kinetic energy profiles exhibited qualitatively good agreement with the experimental measurements, while the DDES model results agreed less well. Simulations using the Detached Eddy Simulation (DES) model, DDES model, and the new HRL model were performed for the flow field analysis of the airfoil with ice shape. Computations of DES, DDES, and new HRL model are still not rigorously comparable to the experiments as these computations have not yet attained statistically stationary flow fields. However, the qualitative assessment of the computations shows that the new HRL model enhances shear layer breakup and rollup in the separated flow region more so than do either DES or DDES.

Delayed Detached Eddy Simulation (DDES) and Unsteady Reynolds Averaged Navier-Stokes (URANS), based on the two-equation Shear Stress Transport (SST) model, are implemented to investigate the flow features and the aero-optical distortions around the turret. The Mach number is Ma = 0.4 and the Reynolds number is Re = 1.43 × 106. Instantaneous and time-averaged flow fields are presented to compare the ability of DDES and URANS in predicting the flow features. The instantaneous results show that DDES can resolve the abundant flow structures and more disordered density distributions than URANS. The time-averaged pressure coefficient and the density distribution of both methods are generally similar, but the time-averaged turbulent kinetic energy of URANS is far higher than that of DDES. The time-averaged pressure coefficient of DDES is closer to experimental data. In the windward view, typical surface flow features of DDES and URANS are similar. In the leeward view, there are remarkable differences of typical flow features between DDES and URANS. At the six angles of elevation, 60°, 76°, 90°, 103°, 120°, and 132°, the spatial-temporal wavefront distortions are calculated and discussed with the geometric ray-tracing method and the Zernike polynomial fitting, respectively. In spatial distribution, the wavefront distortions of DDES and URANS are slightly different from the experimental data. At the angles of 60°, 76°, 90°, and 103°, the tendencies of wavefront distortion of DDES at different tracing distances are the same with that of URANS, which is due to the same ability of two methods to resolve the density distributions in the attached flow region. However, the results of DDES agree well with the experimental results at the angles of 120° and 132°, which is bigger than the results of URANS. For temporal characteristics, the frequencies of wavefront distortions of DDES are obviously higher than that of URANS. The amplitudes of wavefront distortions by DDES are about 3 to 5 times higher than that by URANS. At the cases of two different FLHs at Ma = 0.4, the flow structures are totally similar, and the tendencies of wavefront distortion with θ are also similar. At the cases of three Mach number, the compression has a big influence on the wavefront distortion.

The far-field noise produced by a Rudimentary Landing Gear (RLG) was investigated using Delayed Detached Eddy Simulation (DDES) coupled with a Ffowcs-Williams Hawkings (FWH) integral. Computational results are presented for the RLG geometry using three unstructured grids of quasi-nested refinement. The geometry consists of a square post attached to an axle supporting four wheels, which is entirely suspended from an inviscid flat plate. The Reynolds number was fixed at 106 based on the wheel diameter and freestream properties. The freestream Mach number was fixed at 0.115. The effect of grid resolution using a low dissipation scheme is examined in terms of both aerodynamic forces as well as acoustic spectra. Flow visualizations reveal rich three-dimensional unsteady content and the pattern of wall-pressure fluctuations are consistent with experimental observations. In general the FWH equation predictions of the far-field noise are in very good agreement with acoustic microphone measurements. From these preliminary results it appears that DDES has the potential to become a viable tool for evaluating low noise gear designs during the early design phases before wind tunnel and flight testing have commenced. Efforts are underway to extend the approach to more complex landing gear geometries.

This study analyzes the influence of Reynolds number on the turbulence anisotropy behavior for the transitional flow over the MTU-T161 linear low-pressure turbine (LPT) cascade. Two operating points at Reynolds number Re = 90,000 and Re = 200,000, both at an isentropic exit Mach number of 0.6, are calculated using a transitional Delayed Detached Eddy Simulation (DDES) model. We focus our investigation on the separation-induced transition occurring on the suction side, its sensitivity to the Reynolds number and the capabilities of the transitional DDES approach for capturing the turbulent state. The computational model of the MTU-T161 cascade consists of a single blade passage, including the diverging viscous sidewalls. Synthetic turbulence is generated at the inlet of the domain to mimic realistic turbomachinery flow conditions. We show that the transitional DDES model is able to capture the separation and transition mechanism correctly for both Reynolds numbers, when compared to experimental data. The main part of this paper consists of a detailed analysis of the turbulence anisotropy behavior with particular attention to the separation bubble when changing the Reynolds number. By increasing the Reynolds number from 90,000 to 200,000, the turbulence anisotropy state of the suction side flow changes only slightly. At the higher Reynolds number, the passage flow is mostly governed by two-component turbulence state, while the separation bubble and its influence on the passage flow become weaker. The turbulence anisotropy analysis reveals an almost two-component state very close to the wall region and a one-component turbulence state in the separated shear layer for both Reynolds numbers. Our results show the capability of the transitional DDES model to capture the correct trend of the Reynolds stresses and the anisotropy behavior by comparing the results to a previously published Large eddy simulation (LES). The DDES method is not successful in capturing the Klebanoff modes (streamwise fluctuations) in the pre-transitional region, when compared to LES. These results enhance our overall comprehension of the turbulence state within different separation bubble sizes. Furthermore, the results indicate that the transitional DDES model resolves the essential characteristics of turbulence while keeping the computational cost up to seven times lower than LES.

The numerical prediction of transition from laminar to turbulent flow has proven to be an arduous challenge to computational fluid dynamics (CFD). Few approaches can provide routine accurate results within the cost limitations of engineering applications. In the present paper described is the application of a -Re transition model in combination with the delay detached eddy simulation (DDES) and Ffowcs Williams and Hawkings (FW-H) acoustic analogy method to cylinder vortex/vortex induced noise at a subcritical Reynolds number. In the process of numerical simulation, a traditional DDES based on the full-turbulence model SST is carried out for comparison and a 7th-order weighted compact nonlinear scheme (WCNS-E8T7) is adopted to ensure that the physical models are not affected by numerical dissipation or dispersion. In the first case, single cylinder cross-flow at ReD =4.3104 and Ma=0.21, is considered as a benchmarking problem for validating turbulence models and aerodynamic noise prediction methods. Its aerodynamic coefficients, St, CL and CD at root-mean-square (rms) and averaged values are measured by Szepessy and Bearman, while an acoustic measurement was recently made at Ecole Centrale de Lyon. The traditional DDES only based on SST model (SST-DDES) delays the instability of the shear layer on the sides of the cylinder, which leads to the recirculation zone in mean flow to grow and the induced drag to increase. Moreover, the vortex shedding frequency predicted by SST-DDES is larger than the actual value, which makes the whole sound pressure level (SPL) spectrum move toward high frequency region. However, combining the -Re transition model, the DDES (called Tran-DDES in the present article) can give the results in good agreement with the experimental data. In the second case considered is an airfoil in the wake of the cylinder. The flow condition is similar to that in the first case and the experimental results are also obtained at Ecole Centrale de Lyon. The issue of SST-DDES in recirculation zone in mean flow is weakened, which relates to the interaction between the airfoil and cylinder wake, the prediction of mean flow by SST-DDES is similar to that by the Tran-DDES. But in terms of the rms values of turbulent fluctuation components and SPL, the predictions by Tran-DDES are still better than those by SST-DDES.

Delayed-Detached Eddy Simulation (DDES) is conducted to simulate aerodynamic stall flow over NACA0012 airfoil at 45 ◦ angle of attack. DDES is an improved version of DES97 to avoid Modeled-Stress Depletion (MSD) in attached boundary layer by redefining the length scale of DES97. The test of DDES for the flat plate shows that the delayed LES function facilitates DDES to preserve eddy viscosity even with a severe grid that makes DES to undergo MSD. For comparison, DES97 and URANS also were conducted for the stalled NACA 0012 airfoil flow. DDES and DES predicted the drag coefficient accurately, while URANS overpredicted the drag by 33.6%. Both DES and DDES appear to be satisfactory to simulate the stalled airfoil flow at high angle of attack, in which the large structure of vortex are dominant.

Transonic wing stall of a blended flying wing common research model based on DDES method

In the present study, the subcritical flow past a generic side mirror on a base plane is investigated at the Reynolds number of 5.2×105 using delayed detached eddy simulation (DDES) turbulence model. Asides from the capability of capturing main features of the large recirculation vortex in the wake of the side mirror and the front horseshoe vortex, the accuracy of DDES estimation of recirculation length is significantly increased by over 20%, compared to the detached eddy simulation (DES) estimation using the same grid. And DDES prediction of pressure coefficient at the trailing edge of the mirror is in good agreement with the experiments, which is more accurate than both DES and large eddy simulation (LES) results. The results verify the capacity of DDES turbulence model to solve the turbulent flow around the side mirror. This is a key foundation for possible future study of full simulation of external flow field of vehicle.

Implementation of Delayed Detached Eddy Simulation method to a high order spectral difference solver

This paper investigates the turbulent flow and aerodynamic noise of a half-cylinder body mounted on a flat plate at using high-order cell-centred finite difference method with delayed detached-eddy simulation (DDES) and large-eddy simulation (LES). Transient flow patterns from the two simulations are found to be very different in consideration of the small-scale structures. The profiles of mean velocity, resolved turbulent kinetic energy and resolved Reynolds shear stress are found to be similar among all the simulations, indicating mean quantities are relatively insensitive to turbulence modelling and grid resolution. The power spectra density of the pressure fluctuations show that LES is more capable of resolving energies in high-frequency range than DDES. After computing the normalised wavenumber-frequency spectra of fluctuating pressure on the window, we further carried out the wavenumber-frequency decomposition to separate the acoustic and the hydrodynamic components from the pressure fluctuations. The energy distribution shows that the acoustic energy has a much slower decaying rate in the high-frequency range than the hydrodynamic energy. In addition, the space-averaged sound pressure levels of pressure fluctuations on the window indicate that the present simulation with a high-order method is able to improve the accuracy in predicting pressure spectra. Finally, we carry out proper orthogonal decomposition to extract the dominating features of the decomposed acoustic and hydrodynamic components of pressure fluctuation. Patterns of multi-scale turbulence in hydrodynamic modes and propagating wavefronts of cylinder shape in acoustic modes are identified. The present research indicates that a relatively coarse grid is still capable of resolving fluctuating quantities of energy-containing structures, and LES is suggested against DDES when near-wall aerodynamic noise is the main concern.