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A general construction approach for a class of detached-eddy simulation (DES) methods with the turbulent length-scale equation is presented in this study. It supports the rationality of the construction and provides a theoretical estimation of the model coefficients in DES simulation. By using the construction approach, a differential Reynolds-stress model (RSM), referred to as Speziale-Sarkar-Gatski (SSG)/Launder–Reece–Rodi (LRR)-ω RSM, is built into the improved delayed DES (IDDES) method. After calibration of the model parameters in the IDDES method and basic validation for decaying isotropic turbulence, the RSM-based IDDES approach is then applied to simulate the massively separated flows around the tandem cylinders and the transonic buffet flow over a hammerhead launch vehicle. The simulations are validated by the available experimental data, and the performance is evaluated by means of instantaneous, statistical, spectral analysis of the numerical data. It is found that the RSM-based IDDES method shows better performance comparing with the k-ω shear-stress transport (SST)-based IDDES method, especially for predicting the development of massively separated flows behind the bluff body.

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... The conventional DES adopts a Smagorinsky-like subgrid-stress model in the LES region away from the wall. The scale coefficient CS in the Smagorinsky subgrid model [23] is a function of the model constant CDES in the DES [20], and CDES is usually determined by numerical calibration of canonical turbulence case (e.g., decaying isotropic turbulence). Canuto and Cheng et al. [24] found that CS should not be a uniform constant but a parameter that needs to be adjusted according to the flow state. ...

... As mentioned above, the RSM-based DES methods have shown advantages over the DES method under the framework of the eddy-viscosity model in many studies [18,20,37]. However, the existing RSM-based DES still adopts the classical Smagorinsky model in the LES region. ...

... method. To further investigate the turbulence resolution of the RSM-DynIDDES in the region far from the wall, we also adopted the simulation results by the RSM-IDDES presented in Ref. [20] for comparison. Ref. 20 has examined that this grid can resolve more than 80% of the turbulent kinetic energy in the flow separation zone, which is sufficient for the DES simulation [59]. ...

A dynamic version of the improved delayed detached-eddy simulation (IDDES) based on the differential Reynolds-stress model (RSM), referred to as the RSM-DynIDDES, is developed by applying the dynamic Smagorinsky subgrid model to the large eddy simulation (LES) branch of the IDDES. The RSM-DynIDDES simulates the periodic hills flow after a basic numerical validation for the decaying isotropic turbulence simulation. Well-predicted velocity profiles and Reynolds stress distributions are obtained by the RSM-DynIDDES in the periodic hills flow. The simulation results indicate that the RSM-DynIDDES can capture more small-scale vortex structures in the LES region away from the wall than the original RSM-based IDDES (RSM-IDDES). The RSM-DynIDDES is also employed in simulating the transonic buffeting of a launch vehicle with a payload fairing. The numerical results have been compared with that of the RSM-IDDES. It is found that the RSM-DynIDDES can improve turbulence resolution in the off-wall region while retaining the advantages of the original RSM-IDDES in simulating the instability process of the free shear layer.

... A further attempt [26] to use RSM with IDDES to simulate a periodic channel flow in combination with a suitable low-dissipative numerical scheme showed some potential, but the overall approach was not sufficiently validated for fundamental test cases, like decaying isotropic turbulence (DIT). More recently, Wang et al. [27] published an IDDES based on the SSG/LRR-RSM of Eisfeld et al. [17] (also used in this work), following a similar direct coupling strategy as originally proposed by Probst et al. [22] for RSMbased DDES and later adopted by [26] and e.g. [21]. ...

... pointed out by [13,28]. In this regard, it should be noted that Wang et al. [27] do not provide fundamental validation studies of their RSM-IDDES in WMLES mode, e.g. for the periodic channel flow. ...

... A further attempt [26] to use RSM with IDDES to simulate a periodic channel flow in combination with a suitable low-dissipative numerical scheme showed some potential, but the overall approach was not sufficiently validated for fundamental test cases, like decaying isotropic turbulence (DIT). More recently, Wang et al. [27] published an IDDES based on the SSG/LRR-ω RSM of Eisfeld et al. [17] (also used in this work), following a similar direct coupling strategy as originally proposed by Probst et al. [22] for RSM-based DDES and later adopted by [26] and e.g. [21]. ...

... pointed out by [13], [28]. In this regard, it should be noted that Wang et al. [27] do not provide fundamental validation studies of their RSM-IDDES in WMLES mode, e.g. for the periodic channel flow. ...

A novel variant of Improved Delayed Detached-Eddy Simulation based on a differential Reynolds-stress background model is presented. The approach aims to combine the advantages of anisotropy-resolving Reynolds-stress closures in the modelled RANS regions with consistent LES and wall-modelled LES behaviour in the resolved flow regions. In computations of decaying isotropic turbulence with a low-dissipative flow solver it is shown that a straightforward hybridized Reynolds-stress model provides insufficient turbulent dissipation as sub-grid closure in the LES regions and is therefore locally replaced by scalar viscosity modelling. Simulations of periodic channel flows at different Reynolds numbers and grid resolutions are used to calibrate and validate the wall-modelled LES branch of the new model. A final application in embedded wall-modelled LES of a flat-plate boundary layer is widely consistent with results using the SST-RANS background model, but shows some deviations from the Coles-Fernholz skin-friction correlation. In this regard, initial sensitivity studies indicate possible adverse effects due to the synthetic-turbulence approach used in these simulations.

... The dissipation of turbulent kinetic energy via turbulent flow serves as a bridge between Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES). This ensures the return of the original model in the RANS region and allows for the Smagorinsky sub grid scale stress model to be obtained under the assumption of turbulent equilibrium in the LES region [42]. 3 4 RANS region : ...

Shock wave/turbulent boundary layer interaction (SBLI) is one of the most common physical phenomena in transonic wing and supersonic aircraft. In this study, the compression ramp SBLI (CR-SBLI) was simulated at a 24° corner at Mach 2.84 using the open-source OpenFOAM improved delayed detached eddy simulation (IDDES) turbulence model and the “Rescaling and Recycling” method at high Reynolds number 1.57×106. The results of the control effect of the jet vortex generator on CR-SBLI showed that the jet array can effectively reduce the length of the separation zone. The simulation results of different jet parameters are obtained. With the increasing jet angle, the reduction in the length of the separation zone first increased and then decreased. In this work, when the jet angle was 60°, the location of the separation point was x/δ=−1.48, which was smaller than other jet angles. The different distances of the jet array also had a great influence. When the distance between the jet and the corner djet=70 mm, the location of the separation point x/δ=−1.48 was smaller than that when djet=65/60 mm. A closer distance between the jet hole and the corner caused the vortex structures to squeeze each other, preventing the formation of a complete vortex structure. On the other hand, when the jet was farther away, the vortex structures could separate effectively before reaching the shock wave, resulting in a better inhibition of SBLI. The simulation primarily focused on exploring the effects of the jet angle and distance, and we obtained the jet parameters that provided the best control effect, effectively reducing the length of the CR-SBLI separation zone.

... Current advanced turbulence modelling methods like hybrid RANS/LES are able to predict the unsteady pressure field for a complex configuration with a given fidelity level. 19,33,34 However, they are still costly in terms of computational time and resources, especially applied to realistic, high Reynolds flows. In the earlier phases of design, surrogate models could help providing insights into the unsteady wall-pressure field, namely the local root-mean-square pressure coefficient and the single-point wall-pressure spectrum. ...

Convolutional neural networks (CNNs) are used to predict the fluctuating wall-pressure coefficient and associated single-point pressure spec-
tra in the separating/reattaching flow region around a generic space launcher configuration in the transonic regime. The neural networks are
trained on a generic axisymmetric afterbody configuration. A Zonal Detached Eddy Simulation of a semi-realistic launcher geometry [NASA
(National Aeronautics and Space Administration) model 11 hammerhead] is performed and validated using available experimental results.
This configuration is used as a testing case for the trained models. It is shown that the CNNs are able to identify flow features related to phys-
ical phenomena of the flow. From this feature identification, the models are able to predict the evolution of fluctuating wall quantities and
locate the regions of high pressure fluctuations. A scaling procedure is proposed to retrieve correct levels of the predicted quantities for a
given unknown configuration having different free stream conditions. We also demonstrate that the present models perform well applied on
Reynolds-Averaged Navier–Stokes mean flow fields, paving the way for a significant reduction in the computational cost for predicting wall-
pressure fluctuations around space launchers.

This paper presents a neural network-based turbulence modeling approach for transonic flows based on the ensemble Kalman method. The approach adopts a tensor basis neural network for the Reynolds stress representation, with modified inputs to consider fluid compressibility. The normalization of input features is also investigated to avoid feature collapsing in the presence of shock waves. Moreover, the turbulent heat flux is accordingly estimated with the neural network-based turbulence model based on the gradient diffusion hypothesis. The ensemble Kalman method is used to train the neural network with the experimental data in velocity and wall pressure due to its derivative-free nature. The proposed framework is tested in two canonical configurations, i.e., 2D transonic flows over the RAE2822 airfoils and 3D transonic flows over the ONERA M6 wings. Numerical results demonstrate the capability of the proposed method in learning accurate turbulence models for external transonic flows.

Many engineering applications involve turbulent flows around bluff bodies. Because of their intrinsically unsteady dynamics, bluff body characteristic flows feature unique turbulence-related phenomena, which makes their numerical modeling challenging. Accordingly, accounting for a circular bluff body flow configuration, three different turbulence modeling approaches are investigated in this work, (i) Reynolds-averaged Navier–Stokes (RANS), (ii) large eddy simulation (LES), and (iii) hybrid RANS/LES. Regarding the hybrid approaches, two variants of the detached eddy simulation (DES) one, delayed DES (DDES) and improved delayed DES (IDDES), are studied. As RANS model, the k−ωSST
is utilized here. This RANS model is also used as the background one for both DDES and IDDES. Wall-adaptive local eddy viscosity (WALE) is used in turn as the sub-grid scale (SGS) model for LES. The velocity two-point correlation function is used to assess the mesh size requirements. When compared to experimental data, the obtained numerical results indicate that RANS overestimates the recirculating bubble length by over 18% and is not capable of describing the turbulent kinetic energy and the flow anisotropy in agreement with the experimental data. In contrast, LES, DDES, and IDDES are all within 1% of the recirculating bubble length while predicting both the Reynolds stress tensor components and the corresponding flow anisotropy in agreement with the measurements. Besides, normalized anisotropy tensor invariants maxima in the shear layer were reproduced by all scale resolving models studied here, but they failed to yield the local extrema measured within the wake recirculation region. A comparative analysis of the anisotropic Reynolds stress tensor invariances underscores the adequacy of the scale resolving models.
Full text available at: https://rdcu.be/c8p9M

Direct stability analysis based on the Floquet theory has been employed to clarify the effects of planar shear on three-dimensional instabilities in the wake of two identical circular cylinders of diameter D in tandem arrangement. The center-to-center separation (Lx) in the range of 1.2 ≤ Lx/D ≤ 2.5 was considered. The onset of the three-dimensional instabilities was calculated, and the critical Reynolds number and corresponding spanwise wavenumber varying with the separation were discussed for different shear rates. Representative configurations were chosen to illustrate different transition scenarios, with the three-dimensional instabilities studied in detail for each case. It was found that three different effects of planar shear on the three-dimensional synchronous instability originally present in the otherwise uniform flow were identified depending on the separation. A subharmonic mode referred to as mode SS was observed to develop in the wake due to the flow asymmetry caused by the planar shear. This subharmonic mode differs from the C-type mode in terms of both the spatial structure and critical spanwise wavelength. Furthermore, the mode SS instability was found to be intensified as the shear becomes stronger, and it develops more rapidly than the synchronous modes.

A novel method is proposed to combine the wall-modeled large-eddy sim-ulation (LES) with the diffuse-interface direct-forcing immersed boundary (IB) method. The new developments in this method include: (i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model; (ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.

Wall-modeled large-eddy simulation is employed in combination with the FfowcsWilliams-Hawkings equation to predict and analyze the aeroacoustics of a 30P30N three-element airfoil. The results are compared with experimentalmeasurements, and quantitative agreement is obtained in terms of flowstatistics, frequency spectra of pressure fluctuations on the slat surface, and the far-field noise spectra, thus demonstrating the feasibility and accuracy of the wall-modeled large-eddy simulation approach. The slat cove is confirmed to be the primary sound source and emits narrowband tonal noise at several resonance frequencies in addition to broadband noise. The main element is the largest contributor to low-frequency noise, and the flap is a negligible noise source at all frequencies. Computational results for different freestreamMach numbers indicate that the resonance frequencies are well predicted by the semi-empirical models of Block ("Noise Response of Cavities of Varying Dimensions at Subsonic Speeds," NASA Technical Note D-8351, 1976) and Terracol et al. ("Investigation of the Unsteady Flow and Noise Generation in a Slat Cove," AIAA Journal, Vol. 54, No. 2, 2016). The intensity of flyover noise is shown to largely scale with the fifth-power of Mach number, as suggested by Guo and Joshi ("Noise Characteristics of Aircraft High Lift Systems," AIAA Journal, Vol. 41, No. 7, 2003), but in most other directions, the Mach number scaling of sound intensity is higher than the fifth power.

The paper addresses the issue of the significant delay of transition from RANS to LES in shear layers, which is known to affect the original version of Detached-Eddy Simulation (DES) on typical anisotropic grids. A common remedy has been to disable the subgrid scale model, leading to Implicit LES (ILES). Here, enhanced versions of DES are proposed based on new definitions of the subgrid length-scale. Unlike the original definition attached to DES (i.e., simply the maximum local grid spacing) the new ones include solution-dependent kinematic measures which serve as indicators of the nearly 2D grid-aligned flow regions which are typical of the initial region of free and separated shear layers. This brings about a significant reduction of the subgrid viscosity in such regions. This, in turn, unlocks the Kelvin-Helmholtz instability and drastically speeds-up transition to 2D and then 3D flow structures in shear layers. At the same time, the proposed length-scale is not influenced by the smallest grid dimension, unlike the cube root of the cell volume and other recently proposed definitions, and we view this as a physically plausible, safe and therefore preferable length-scale definition. The advantages of these enhanced versions are demonstrated on a set of numerical examples which include isotropic turbulence, a mixing layer, a jet, a boundary layer, and a backward-facing step. The new definitions are as successful as ILES in liberating the early instabilities, while being non-zonal and compatible with later interactions of the turbulent region with solid bodies. The turbulence statistics of the flows and the radiated noise of the jet are also considerably improved, especially with relatively coarse lateral grid spacings. The new definitions will also improve LES, particularly with the Smagorinsky model.

The objective of this paper is to assess and compare several self-adapting hybrid RANS/LES
models for a backward facing step
flow, in conjunction with a high-order finite volume numerical scheme well suited for scale-resolving simulations. The most promising model is
then applied to an axisymmetric backward facing step, representative of the base flow
behind a launcher. Present computations provide a satisfactory representation of the characteristic
flow frequencies. Finally, the proposed methodology is applied to the computation
of the flow behind the Ariane 5 space launcher to demonstrate its applicability to complex
flow configurations of industrial interest.

Three spatial schemes, the original Roe scheme and two high-order symmetric total variation diminishing schemes, whose dissipations are multiplied by a constant parameter or a function (called 0), are coupled with delayed detached eddy simulation to investigate the numerical dissipation effects on the massive separation flow around tandem cylinders. From the comparisons between the computations and the available measurements, the numerical dissipation has a significant influence on the mean and instantaneous flowfields. The original Roe scheme is too dissipative to predict the small scale turbulent structures, and it strongly suppresses the growth of resolved turbulence. The S6WENO5 schemes with constant-phi and adaptive-phi times of dissipation have similar performances and they well match the measurements. However, the S6WENO5 with constant-phi times (0.12 here) of dissipation is too empirical, and the small constant-phi times of dissipation cannot generally suppress the numerical oscillations near the wall and in the far fields. The S6WENO5 with adaptive dissipation provides the best performance.

Flow and noise predictions for the tandem cylinder benchmark are performed using lattice Boltzmann and Ffowcs Williams–Hawkings methods. The numerical results are compared to experimental measurements from the Basic Aerodynamic Research Tunnel and Quiet Flow Facility (QFF) at NASA Langley Research Center. The present study focuses on two configurations: the first configuration corresponds to the typical setup with uniform inflow and spanwise periodic boundary condition. To investigate installation effects, the second configuration matches the QFF setup and geometry, including the rectangular open jet nozzle, and the two vertical side plates mounted in the span to support the test models. For both simulations, the full span of 16 cylinder diameters is simulated, matching the experimental dimensions. Overall, good agreement is obtained with the experimental surface data, flow field, and radiated noise measurements. In particular, the presence of the side plates significantly reduces the excessive spanwise coherence observed with periodic boundary conditions and improves the predictions of the tonal peak amplitude in the far-field noise spectra. Inclusion of the contributions from the side plates in the calculation of the radiated noise shows an overall increase in the predicted spectra and directivity, leading to a better match with the experimental measurements. The measured increase is about 1 to 2 dB at the main shedding frequency and harmonics, and is likely caused by reflections on the spanwise side plates. The broadband levels are also slightly higher by about 2 to 3 dB, likely due to the shear layers from the nozzle exit impacting the side plates.

This paper presents a parallel computation with hybrid Reynolds-averaged Navier-Stokes and large eddy simulation methods. Two types of hybrid approaches, referred to as detached eddy simulation and delayed-detached eddy simulation, are investigated through introducing length scales into the weakly nonlinear k-omega turbulence model. Before the implementation of hybrid methods, the baseline weakly nonlinear model and k-omega shear-stress-transport model are validated in the transonic RAE-2822 airfoil and ONERA-M6 wing cases. The numerical results show satisfactory agreement with the available experimental data. The Reynolds-averaged and hybrid methods based on the weakly nonlinear turbulence model are then applied to calculate the high Reynolds number transonic separation flows around NASA TN D-712 wing fulesage For the higher angle of attack case (alpha = 26.2 deg), both hybrid methods deliver good results when compared with the experiment; for the moderate angle of attack case (alpha = 12.5 deg), the results obtained with the delayed detached eddy simulation are satisfactory, whereas the starting point of the wing vortex breakdown predicted with the detached eddy simulation is too far upstream.

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high– Reynolds number, massively separated flows remains, for which DES is con-vincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review dis-cusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of a theoretical order of accuracy. These issues also affect LES in any nontrivial flow. This review also covers the numerical needs of DES, gridding practices, coupling with different RANS models, derivative uses such as wall modeling in LES, and extensions such as zonal DES and delayed DES.

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.
For some research studies in small domains, Δ∥ is made much smaller than δ, and LES content is generated intentionally. However for natural DES applications in useful domains, it is preferable to over-ride the DES limiter and maintain RANS behavior in boundary layers, independent of Δ∥ relative to δ. For this purpose, a new version of the technique – referred to as DDES, for Delayed DES – is presented which is based on a simple modification to DES97, similar to one proposed by Menter and Kuntz for the shear–stress transport (SST) model, but applicable to other models. Tests in boundary layers, on a single and a multi-element airfoil, a cylinder, and a backward-facing step demonstrate that RANS function is indeed maintained in thick boundary layers, without preventing LES function after massive separation. The new formulation better fulfills the intent of DES. Two other issues are discussed: the use of DES as a wall model in LES of attached flows, in which the known log-layer mismatch is not resolved by DDES; and a correction that is helpful at low cell Reynolds numbers.

A CFD strategy is proposed that combines delayed detached-eddy simulation (DDES) with an improved RANS-LES hybrid model aimed at wall modelling in LES (WMLES). The system ensures a different response depending on whether the simulation does or does not have inflow turbulent content. In the first case, it reduces to WMLES: most of the turbulence is resolved except near the wall. Empirical improvements to this model relative to the pure DES equations provide a great increase of the resolved turbulence activity near the wall and adjust the resolved logarithmic layer to the modelled one, thus resolving the issue of “log layer mismatch” which is common in DES and other WMLES methods. An essential new element here is a definition of the subgrid length-scale which depends not only on the grid spacings, but also on the wall distance. In the case without inflow turbulent content, the proposed model performs as DDES, i.e., it gives a pure RANS solution for attached flows and a DES-like solution for massively separated flows. The coordination of the two branches is carried out by a blending function. The promise of the model is supported by its satisfactory performance in all the three modes it was designed for, namely, in pure WMLES applications (channel flow in a wide Reynolds-number range and flow over a hydrofoil with trailing-edge separation), in a natural DDES application (an airfoil in deep stall), and in a flow where both branches of the model are active in different flow regions (a backward-facing-step flow).

It is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws. The grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh.

Unsteady turbulent separated flow widely exists in aerospace vehicles and has become a major research topic. For the precise turbulent flow prediction, efficient and accurate numerical methods are the premise and foundation. However, most shock-capturing schemes designed for compressible flows have some difficulties in low-speed flow regions, and reduce the reliability when simulating unsteady turbulent separated flow with rich low Mach number features. Thus, the paper proposes a high-fidelity low-dissipation scheme termed LD-Roe2 and investigates the performances of the novel approach in unsteady turbulent separated flow simulations using the Hybrid Reynolds Averaged Navier-Stokes Equations/Large Eddy Simulation Approach (Spalart-Allmaras Delayed Detached Eddy Simulation). Numerical results including flow over a circular cylinder at subcritical Reynolds number and flow over tandem cylinders, demonstrate that the novel low-dissipation scheme can better simulate the unsteady separated flow and depicts finer smaller-scale vortical structures compared with traditional numerical schemes. It is expected to provide a more accurate and applicable numerical solution for the refined turbulent prediction.

The hybridization of Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) methods is seen to be the most promising way to efficiently deal with separated turbulent flow simulations relevant to aerospace and wind energy applications. Characteristic conceptual features of popular hybrid RANS-LES and their applications to hill-type and airfoil flow including flow separation are described. Conceptual questions on existing hybrid RANS-LES are pointed out and ways to overcome these problems are presented. Further analyses show that corresponding novel hybrid RANS-LES methods generalize and improve existing methods. The discussions reveal, in particular, the great value of physical and mathematical realizability constraints for the substantial improvement of simulation methods.

A length-scale correction recently developed for the SSG/LRR-ω Reynolds-stress model is applied to the flow around airfoils near maximum lift and the transonic flows around a wing and a generic aircraft with shock-induced separation. The length-scale correction is active only in regions of separation. It reduces the predicted maximum lift of airfoils by widening the separation bubble at the trailing edge, and predicts an increased size of shock-induced separation regions.

An extensive wind tunnel test campaign devoted to the characterization of the aerodynamic and aeroacoustic behaviour of the new Space Launcher VEGA-C has been carried out in the trisonic wind tunnel available at the National Institute for Aerospace Research (INCAS) in Bucharest. The present paper summarizes the main results of the aeroacoustic investigation with a specific focus on the buffeting analysis. For this reason, the results presented herein are limited to the transonic conditions which are the most critical in terms of occurrence of flow instabilities. The scaled instrumented model of the VEGA-C launcher has been equipped with flush mounted Kulite sensors that provided the distribution of the wall pressure fluctuations. Pressure measurements at the wall of the wind tunnel have been carried out as well, with the scope of measuring reference signals to be used for cleaning the model pressure data from the back-ground noise. Numerical simulations have been also performed to facilitate the physical interpretation of the experimental outcomes by qualitatively identifying the position of the shockwaves and tracking their evolution along the launcher for increasing Mach number. Data processing provides temporal statistics of the wall pressure signals as well as spectral quantities that give clear indications about the absence of buffeting.

During ascent of launcher, the unsteady aerodynamic loads associated with transonic buffet flow have become of considerable concern. To study the unsteady dynamics of buffet flow, delayed detached-eddy simulations of a hammerhead configuration have been conducted at transonic Mach numbers. The results, including mean Cp, Cprms, PSD and Schlieren visualizations, were validated by the measurements obtained from the wind-tunnel experiments. Nevertheless, to perform a good validation for unsteady loads, the numerical data needed to be filtered according to the data acquisition used in the experiments. The studies were performed by means of instantaneous, statistical, spectral and cross-spectral analysis of the numerical data, which identify the fluid dynamic mechanism that produces a relatively strong buffet environment. The mechanism involves a sequence of vortex, which is shed downstream, merges together, and ultimately impinges on the wall leading to large fluctuations. Besides, the cross-spectral analysis also revealed that the subsequent large scale and low frequency vortex shedding of the developed shear layer provides a strong influence on the flows around cone–cylinder conjunction. The fluctuations in this area are highly sensitive to Mach numbers, and the peak of Cprms appears at Ma ≈ 0.81.

The pitching moments of a fighter model at an incidence of 32° without and with nine airbrakes are simulated by solving the unsteady Reynolds-averaged Navier–Stokes equations. The maximum reduction (60.22%) of the total pitching moment is obtained by the airbrake with deflection angle of 60° and length of 0.115 times the wing span. Furthermore, the unsteady flowfields are predicted by the improved delayed detached-eddy-simulation model. The breakdowns of the forebody and strake vortices are advanced, and the flow is blocked by the airbrake, jointly leading to a reduction of the pitching moment. Surprisingly, the pressure fluctuations on the oblique vertical tail are also attenuated due to the existence of the airbrake. A maximum reduction of overall sound pressure level by 11.8 dB is found near the leading-edge on the outer surface of the vertical tail due to the use of the 60T1 airbrake. The bursting vortices from the forebody and strake move towards the symmetry plane owing to the low-pressure region after the airbrake, weakening the unsteady interactions between the bursting vortices and oblique vertical tail.

The current study developed a new dynamic delayed detached-eddy simulation (dynamic DDES) model based on the k-ω SST model and the well-established dynamic k-equation subgrid-scale model. Instead of using a constant model coefficient CDES in traditional DES formulations, the present model employs two coefficients Ck and Ce, which are computed dynamically by taking into account the spatial and temporal variations of the flow field at the grid and test filter levels. A modification on shielding function fd is proposed, with a spatial uniformization operator imposed on the velocity gradient to obtain a smooth and monotonous hybrid interface. A damping function φd is introduced based on the local grid resolution and flow condition to damp the Reynolds-averaged Navier-Stokes (RANS) region and achieve wall-modeled LES (WMLES) mode dynamically. The test of the model in developed channel flow shows the log-layer mismatch (LLM) problem is significantly improved with respect to the dynamic LES model and original DDES model. The use of the spatial uniformization operator and the damping function convincingly demonstrates the improvement in prediction of separated flows, with the model coefficients dynamically computed. The LES region is maximized at the limit of grid resolution and more turbulent vortical structures are resolved. The test in the ribbed channel flow shows the present model has considerably better performance in prediction of the mean and turbulence velocity in the strong shear layer and the recirculation bubble. In addition, the simulation of impinging jet shows the model exhibits rapid switching from the RANS to LES under the flow instabilities when the inflow does not include turbulence content.

Full seven-equation Reynolds stress turbulence models are promising tools for todays aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

The procedure of incorporating the detached eddy method and a model of laminar-turbulent transition into the SSG/LRR-ω turbulence model is presented. The approach proposed can be regarded as the generalization of the existing models intended to perform calculations with the SST turbulence model to the case of their use with the SSG/LRR-ω model. The advantage of the approach developed over the RANS turbulence models based on the Boussinesq hypothesis is demonstrated with respect to the problems of flow past an airfoil and cold jet outflow.

For the flow over curved surfaces, an extra wall-normal pressure gradient is imposed to the flow through excessive surface pressure, such that the flow turns in alignment with the surface. In turn, turbulent fluctuations are suppressed over the convex surface; whereas, they are enhanced over the concave. Recently, the direct numerical simulation (DNS) of turbulent channel flow experiencing a 60 degree circular bend shows highly complex flow phenomena. Particularly, the mean flow properties are directly related to the channel geometry; in the impulse response of the mean flow to the step change of streamline curvature, sudden changes in mean strain rate and extra rates of strain emerge. This mean flow process is prior to the response of the turbulence structures. Due to the large streamline curvature, the underlying turbulence lagging mechanism and the stress strain misalignment are difficult to model. For this, the new DNS data for the wall bounded flow with high streamline curvature and large integral length scales is used to explore RANS performance. For eddy-viscosity models, this leads to the Boussinesq approximation being questionable. Also, for a Reynolds-stress model (RSM) with closure approximations applicable to homogeneous turbulent flows that are nearly in equilibrium, the current case can result in substantial predictive error. This is because of, for example, the linear approximation for the rapid pressure-strain correlation. To help move towards better turbulence modelling, Reynolds-averaged Navier-Stokes (RANS) predictions are compared for the same flow configuration as the DNS, using some popular turbulent models. These models include the second-order closure with the stress-ω formulation, the standard k−ω and the Menter’s shear-stress transport (SST) models, the standard Spalart-Allmaras (S-A) model with and without the corresponding strain-vorticity correction. As expected, overall, the RSM provides closer predictions to the DNS data than the selected eddy-viscosity models, even though the predictive accuracy needs to be further improved. Potentially, a non-linear constitutive relation or second-order closure, incorporating a relaxation approximation for the lagging mechanism, may lead to a remedy for the current non-equilibrium flow. Moreover, all models would also benefit from sensitisation to the impact of the large integral length scales.

Space-time correlation measurements in the roughly isotropic turbulence behind a regular grid spanning a uniform airstream give the simplest Eulerian time correlation if we choose for the upstream probe signal a time delay which just ‘cancels’ the mean flow displacement. The correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency ([similar] wave-number at these small turbulence levels). With plausible scaling of the time separations, a scaling dependent on both wave-number and time, it is possible to effect a good collapse of the correlation functions corresponding to wave-numbers from 0·5 cm−1, the location of the peak in the three-dimensional spectrum, to 10 cm−1, about half the Kolmogorov wave-number. The spectrally local time-scaling factor is a ‘parallel’ combination of the times characterizing (i) gross strain distortion by larger eddies, (ii) wrinkling distortion by smaller eddies, (iii) convection by larger eddies and (iv) gross rotation by larger eddies.

Detached Eddy Simulation (DES) based on the k–ω– –f model, termed DES–k-ω– -f, is developed and evaluated in the present study. In this model, the RANS–LES switching is achieved by an adaptation of the turbulent length scale between the LES and RANS regions. The SGS model coefficient is calibrated by the decaying homogeneous isotropic turbulence (DHIT). The capabilities of the proposed model are evaluated on various geometries, i.e. the plane channel flow, wavy channel flow and two side by side square cylinders. The DES results are compared with the URANS and LES results obtained in the present study and the available results obtained in other references. A good agreement is found between the results of the proposed DES model and the LES for three flow configurations employed. For the cases with flow separation, the DES model demonstrates accurate predictions in reproducing the resolved flow and turbulence quantities in comparison with full-resolved LES.

A joint computational and experimental study has been performed at NASA Langley Research Center to investigate the unsteady flow generated by the components of an aircraft landing gear system. Because the flow field surrounding a full landing gear is so complex, the study was conducted on a simplified geometry consisting of two cylinders in tandem arrangement to isolate and characterize the pertinent flow phenomena. This paper focuses on the experimental effort where surface pressures, 2-B Particle Image Velocimetry, and hot-wire anemometry were used to document the flow interaction around the two cylinders at a Reynolds Number of 1.66 × 10 5, based on cylinder diameter, and cylinder spacing-to-diameter ratios, L/D, of 1.435 and 3.70. Transition strips were applied to the forward cylinder to produce a turbulent boundary layer upstream of the flow separation. For (these flow conditions and L/D ratios, surface pressures on both the forward and rear cylinders show the effects of L/D on flow symmetry, base pressure, and the location of flow separation and attachment. Mean velocities and instantaneous vorticity obtained from the PFV data are used to examine the flow structure between and aft of the cylinders. Shedding frequencies and spectra obtained using hot-wire anemometry are presented. These results are compared with unsteady, Reynolds-Averaged Navier-Stokes (URANS) computations for the same configuration in a companion paper by Khorrami, Choudhari, Jenkins, and McGinley (2005). The experimental dataset produced in this study provides information to better understand the mechanisms associated with component interaction noise, develop and validate time-accurate computer methods used to calculate the unsteady flow field, and assist in modeling of the radiated noise from landing gears.

The NASA tandem cylinder benchmark case (L/D = 3.7) is studied numerically using novel variants of DES - the Delayed Detached Eddy Simulation (DDES) and the Improved Delayed Deteched Eddy Simulation (IDDES). The flow Mach number is 0.1285 and the Reynolds number is set to 166.000 to match th corresponding experiments at the NASA Langley Research Center (Jenkins et al., Lockard et al.). Incompressible simulations are carried out on a mandatory grid from the EC ATAAC project with approx. 9.5 million cells with a spanwise extent of 3.0D and flow normal domain extent of approx. 17.8D with symmetry boundary condition to mimic the closed experimental test section. In a second step a compressible IDDES simulation is done to evaluate the broadband noise of the configuration. Measurements are available from the QFF open jet facility. To capture the installation effects a combined grid of above mentioned cylinder core grid and a single stream jet grid is used. The communication between the grids is done by an overset chimera technique. The noise in the far field is calculated by a standard FW-H method. The IDDES approach is designed to extend the LES region of the original DES approach (hybrid RANS/LES) from Spalart et al. (1997) to the turbulent boundary layer, as proposed first by Travin et al. in 2006. The non-zonal blending occures therefore inside the boundary layer - the RANS model acts as a wall model for the LES. The comparison of the simulations show the improvement of the results by using a IDDES.

A comparison of two differential Reynolds-stress models for aeronautical flows is presented. The model herein combines the Speziale-Sarkar-Gatski pressure-strain model with the Launder-Reece-Rodi model toward the wall, where the length scale is supplied by Menter's baseline equation. The epsilon h model from Jakirli and Hanjali has been particularly designed for representing the correct near-wall behavior of turbulence and has been adapted to aeronautical needs. Its length scale is provided by a transport equation for the homogeneous part of the dissipation rate. The models are applied to a series of test cases relevant to aeronautics, showing improved predictions compared to eddy-viscosity models particularly in case of axial vortices.

A Reynolds stress relaxation model, specifically the lag Reynolds stress transport model, is applied to a wingtip vortex flow, and its performance is assessed and compared with other aerospace standard turbulence models. A Reynolds stress relaxation model allows for Reynolds stress history effects due to streamline curvature, which are seen to play an important role in the nondiffusive nature of turbulent vortices. This study shows that the lag Reynolds stress transport turbulence model is capable of predicting mean flow results as accurately as those of the well-performing Spalart-Allmaras model with correction for streamline curvature and system rotation. Furthermore, in this wingtip vortex flow, the lag Reynolds stress transport model predicts turbulence quantities more accurately than the rotation/curvature-corrected Spalart-Allmaras model. Although the lag Reynolds stress transport model well predicts this flow, it is more computationally intensive to solve than the rotation/curvature-corrected Spalart-Allmaras model, and it has some deficiencies, such as an inability to independently control the Reynolds stress magnitude and relaxation amount. Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

This paper presents the Reynolds-averaged Navier-Stokes simulations of successive perturbations in supersonic turbulent flows that are normally encountered in a scramjet intake. Two forward-facing ramps are considered in which the flow is turned through 20 deg compression and 20 deg expansion successively. The first ramp is with sharp corners, and the second one is with curved surfaces having the same radii of curvature. A well-validated finite-volume flow solver is used to simulate these test cases. An eddy-viscosity model and two versions of a differential Reynolds stress model are employed in the computations, and detailed comparisons with measured wall pressure, skin friction, velocity profiles, and Reynolds stress profiles downstream of the interaction region are illustrated and discussed. The results represent a contribution to understanding the capability and the limitations of Reynolds-averaged Navier-Stokes turbulence models in predicting these flows.

Hybrid/bridging models that combine the advantages of Reynolds averaged Navier Stokes (RANS) method and large-eddy simulations are being increasingly used for simulating turbulent flows with large-scale unsteadiness. The objective is to obtain accurate estimates of important large-scale fluctuations at a reasonable cost. In order to be effective, these bridging methods must posses the correct "energetics": that is, the right balance between production (P) and dissipation (e). If the model production-to-dissipation ratio (P/ε) is inconsistent with turbulence physics at that cutoff, the computations will be unsuccessful. In this paper, we perform fixed-point analyses of two bridging models - partially-averaged Navier Stokes (PANS) and unsteady RANS (URANS) - to examine the behavior of production-to-dissipation ratio. It is shown that the URANS-(P/ε) ratio is too high rendering it incapable of resolving much of the fluctuations. On the other hand, the PANS-(P/ε) ratio allows the model to vary smoothly from RANS to DNS depending upon the values of its resolution control parameters.

This paper presents computational simulations of the flow over a 50-deg sweep Missile fin for an angle of attack equal to 25 deg. For such an angle of attack, the flow is expected to fully separate. Nevertheless, Reynolds-averaged Navier-Stokes; computations still predict the presence of a leading-edge vortex. Then, hybrid Reynolds-averaged Navier-Stokes/large eddy simulation methods are assessed. In particular, this study focuses oil the delayed-detached eddy simulation and on a proposed extension of this method (EDDES), in which the objective is to accelerate the destruction of the eddy viscosity in large eddy simulation regions. These two methods are assessed in file case of a boundary-layer flow, and it is shown that the extended delayed-detached eddy simulation behaves as the delayed-detached eddy simulation method. Nevertheless, fit the case of a fully separated flow downstream from it backward facing step, the resolved fluctuations obtained with file extended delayed-detached eddy simulation method are in better agreement with the experimental data titan those of the delayed-detached eddy simulation computation. Finally, these two methods improve the description of the How over the missile fin, predicting a fully separated flow. However, the extended delayed-detached eddy simulation ensures a faster development of instabilities than the delayed-detached eddy simulation and the agreement with the pressure distribution obtained with pressure sensitive paint is much better with the proposed modification of delayed-detached eddy simulation.

A zonal detached eddy simulation (DES) method is presented that predicts the buffet phenomenon on a supercritical airfoil at conditions very near shock buffet onset. Some issues concerning grid generation, as well as the use of DES for thin-layer separation, are discussed. The periodic motion of the shock is well reproduced by averaged Navier-Stokes equations (URANS) and zonal DES, but the URANS calculation has needed to increase the angle of attack compared to the experimental value and the standard DES failed to reproduce the self-sustained motion in the present calculation. The main features, including spectral analysis, compare favorably with experimental measurements (Jacquin, L., Molton, P., Deck, S., Maury, B., and Soulevant, D., "An Experimental Study of Shock Oscillation over a Transonic Supercritical Profile," AIAA Paper 2005-4902, June 2005). A very simple model based on propagation velocities yields the main frequency of the motion. As suggested by Lee (Lee, B. H. K., "Transonic Buffet on a Supercritical Airfoil," Aeronautical Journal, May 1990, pp. 143-152), this calculation highlights that upstream propagating waves are generated by the impingment of large-scale structures on the upper surface of the airfoil in the vicinity of the trailing edge. These upstream propagating waves can regenerate an instability leading to a feedback mechanism.

In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

A new model for the transport equation for the turbulence energy dissipation rate
[varepsilon] and for the anisotropy of the dissipation rate tensor [varepsilon]ij,
consistent with the near-wall limits, is derived following the term-by-term approach and using results of
direct numerical simulations (DNS) for several generic wall-bounded flows. Based
on the two-point velocity covariance analysis of Jovanovic, Ye & Durst (1995) and
reinterpretation of the viscous term, the transport equation is derived in terms of the
‘homogeneous’ part [varepsilon]h of the energy dissipation rate. The algebraic
expression for the components of [varepsilon]ij was then reformulated in terms of
[varepsilon]h, which makes it possible to
satisfy the exact wall limits without using any wall-configuration parameters. Each
term in the new equation is modelled separately using DNS information. The rational
vorticity transport theory of Bernard (1990) was used to close the mean curvature term
appearing in the dissipation equation. A
priori evaluation of [varepsilon]ij, as well
as solving the new dissipation equation as a whole using DNS data for quantities other than
[varepsilon]ij, for
flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing
step and in an axially rotating pipe, all show good near-wall behaviour of all
terms. Computations of the same flows with the full model in conjunction with the
low-Reynolds number transport equation for (uiui) All Overbar,
using [varepsilon]h instead of [varepsilon], agree well with the direct numerical simulations.

A new two-equation model is proposed for large eddy simulations (LESs) using coarse grids. The modeled transport equations are obtained from a direct transposition of well-known statistical models by using multiscale spectrum splitting given by the filtering operation applied to the Navier–Stokes equations. The model formulation is compatible with the two extreme limits that are on one hand a direct numerical simulation and on the other hand a full statistical modeling. The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation. The proposed method is applied to a transposition of the well-known k- statistical model, but the same method can be developed for more advanced closures. This approach is intended to contribute to non-zonal hybrid models that bridge Reynolds-averaged Navier–Stokes (RANS) and LES, by using a continuous change rather than matching zones. The main novelty in the model is the derivation of a new equation for LES that is formally consistent with RANS when the filter width is very large. This approach is dedicated to applications to non-equilibrium turbulence and coarse grid simulations. An illustration is made of large eddy simulations of turbulence submitted to periodic forcing. The model is also an alternative approach to hybrid models.

A new variant of delayed detached-eddy simulation (DDES) based on the Low-Re epsilon-h-RSM as RANS background model is presented which is optionally combined with novel algebraic sensors for the RANS/LES switch. The RSM is aimed to improve RANS-mode predictions of pressure-induced separations on smooth surfaces, while the new sensors eval-
uate boundary-layer properties to distinguish between attached and detached flow regions and place the RANS/LES interface at separation onset. After calibration and basic validation for decaying isotropic turbulence, the epsilon-h-based DDES is applied to a backward-facing
step flow with massive separation and compared to experiments. The results are well in line with original DDES and can be further improved by applying stochastic forcing of the turbulent subgrid stresses. For the HGR-01 airfoil at stall, both the RSM-based approach and the algebraic sensors are found essential in capturing separation onset at the trailing
edge and ensuring LES mode in the separated flow. However, the actual DES computations still suffer from under-resolved turbulence in the separated LES region when compared to PIV measurements, which can neither be compensated by stochastic forcing, nor by a different RANS model or a local grid refinement. Thus, the need to extend the present
method by a more sophisticated forcing becomes evident.

The current DLR Computational Fluid Dynamics validation activities in the framework of the AIAA Drag Prediction Workshop are presented. Since the second workshop in 2003 advanced turbulence models have been integrated in the Reynolds-averaged Navier-Stokes solver FLOWer. The hybrid SSG/LRR-omega differential Reynolds stress turbulence model is presented, combining the Launder-Reece-Rodi (LRR) model near walls with the Speziale-Sarkar-Gatski(SSG) model further apart by applying Menter's blending function F_1. Menter's baseline omega-equation is exploited for supplying the length scale. The SSG/LRR-omega model is applied to the DLR-F6 aircraft configuration. Results are presented for a target lift computation at C_L = 0.500 and for lift, drag and moment coefficients in a range of incidence from -3 to 1.5 degrees. In addition to the validation activities the possibility of anew wind tunnel testing of the DLR-F6 was investigated. Because a test at a higher Reynolds-number is of interest the mechanical strength of the model was analysed using the Finite-Element-Method software ANSYS.

As computational fluid dynamics matures, researchers attempt to perform numerical simulations on increasingly complex aerodynamic flows. One type of flow that has become feasible to simulate is massively separated flow fields, which exhibit high levels of flow unsteadiness. While traditional computational fluid dynamic approaches may be able to simulate these flows, it is not obvious what restrictions should be followed in order to insure that the numerical simulations are accurate and trustworthy. Our research group has considerable experience in computing massively separated flow fields about various aircraft configurations, which has led us to examine the factors necessary for making high-quality time-dependent flow computations. The factors we have identified include: grid density and local refinement, the numerical approach, performing a time-step study, the use of sub-iterations for temporal accuracy, the appropriate use of temporal damping, and the use of appropriate turbulence models. We have a variety of cases from which to draw results, including delta wings and the F-18C, F-16C, and F-16XL aircraft. Results show that while it is possible to obtain accurate unsteady aerodynamic computations, there is a high computational cost associated with performing the calculations. Rules of thumb and possible shortcuts for accurate prediction of massively separated flows are also discussed.

The objective of this work is to derive a shock capturing tool able to treat turbulence with minimum dissipation out of the shock for a large-eddy simulation (LES) of the shock/turbulence interaction. The present numerical modeling of the shock/turbulence interaction consists of a second-order finite volume central scheme using a skew-symmetric form, a Jameson's type artificial dissipation, and the filtered structure function model. We focus on two areas to build simulations of increased accuracy: