Turbulent transonic buffet is an aerodynamic instability causing periodic (albeit, often irregular) oscillations of lift/drag in aerospace applications. Involving complex coupling between inviscid and viscous effects, buffet is characterised by shock wave oscillations and flow separation/reattachment. Previous studies have identified both two-dimensional (2-D) chordwise shock-oscillation and three-dimensional (3-D) buffet-/stall-cell modes. While the 2-D instability has been studied extensively, investigations of 3-D buffet have been limited to only low-fidelity simulations or experiments. Due to computational cost, almost all high-fidelity studies to date have been limited to narrow span-widths around 5 % of aerofoil chord length (aspect ratio, ), which is insufficiently wide to observe large-scale three-dimensionality. In this work, high-fidelity simulations are performed up to , on an infinite unswept NASA Common Research Model (CRM) wing profile at $Re=5\times 10^{5}$ . At , intermittent 3-D separation bubbles are observed at buffet conditions. While previous Reynolds-averaged Navier–Stokes (RANS)/stability-based studies predict quasi-simultaneous onset of 2-D- and 3-D-buffet, a case that remains essentially 2-D is identified here. Strongest three-dimensionality was observed near low-lift phases of the buffet cycle at maximum flow separation, reverting to essentially 2-D behaviour during high-lift phases. Buffet was found to become 3-D when extensive mean flow separation was present. At , multiple 3-D separation bubbles form in a spanwise wavelength range $\lambda =1c$ to $1.5c$ . Spectral proper orthogonal decomposition (SPOD) was applied to analyse the spatio/temporal structure of 3-D buffet-cells. In addition to the 2-D chordwise shock-oscillation mode (Strouhal number $St \approx 0.07-0.1$ ), 3-D modal structures were observed at the shock wave/boundary layer interaction at $St \approx 0.002-0.004$ .

OpenSBLI is an automatic code-generation framework for compressible Computational Fluid Dynamics (CFD) simulations on heterogeneous computing architectures (previous release: Lusher et al. (2021) [4]). OpenSBLI is coupled to the Oxford Parallel Structured (OPS) Domain Specific Language (DSL), which uses source-to- source translation to enable parallel execution of the code on large-scale supercomputers, including multi-GPU clusters. To date, OpenSBLI has largely been applied to compressible turbulence and shock-wave/boundarylayer interactions on very simple geometries comprised of single mesh blocks with essentially orthogonal grid lines. OpenSBLI has been extended in this new release to target strongly curvilinear cases, including transonic aerofoils using multi-block grids. In addition to multi-block mesh support, more efficient numerical shock- capturing methods and filters have been added to the codebase. Improvements to post-processing, reduced- dimension data output, and coupling to a modal decomposition library are also included. A set of validation cases are presented to showcase the new code features. Furthermore, state-of-the-art wide-span transonic aerofoil simulations on up to N = 2.5 x10(9) grid points demonstrate that wider aspect ratios can alter buffet predictions and increase the regularity of the low-frequency shock oscillations by accommodating fully-developed trailing edge flow separation. Spectral Proper Orthogonal Decomposition (SPOD) analysis showed that overly-narrow aerofoil simulations contain additional domain-dependent energy content at a Strouhal number of St approximate to 3 associated with wake modes.

Numerical simulations show great potential to reduce the need for costly physical flight testing during takeoff and landing, thereby decreasing the time-to-market for future aircraft. In order to validate computational fluid dynamics results, we often perform wind-tunnel experiments. However, most simulations in the literature are performed at free-air conditions, neglecting confinement effects, and therefore the wind-tunnel data must be corrected based on empirical methods. In the present work, we compare free-air and in-tunnel simulations of NASA's high-lift configuration of the Common Research Model (CRM-HL) and quantify sensitivities for steady Reynolds-averaged Navier-Stokes (RANS)-based methods and unsteady scale-resolving hybrid RANS/large-eddy simulations (HRLESs). Uncertainties associated with the choice of turbulence model, initialization strategies, and boundary conditions are covered. The present study provides valuable lessons learned and contributes toward best practices for in-tunnel simulations. For maximum lift (CL,max) prediction, RANS-based methods lead to nonphysical flow-separation patterns considering both free-air and in-tunnel configurations. We show consistency between in-tunnel and free-air HRLESs in terms of statistical and unsteady characteristics and reasonable agreement with wind-tunnel data. However, in-tunnel simulations increase the levels of complexity considerably and require long initial transients (independent of the initialization strategy). In order to explain persisting differences between simulation and experiment, we require better characterization of wind-tunnel flow conditions.

The work here presented is the first fully three-dimensional (3D) global stability analysis (GSA) investigation aimed at characterizing low-speed stall on a full-aircraft configuration. The High-Lift version of the NASA Common Research Model is investigated at an angle of attack near CL, max. The matrix-free stability approach here used enables GSA to be carried out on 3D complex geometries and grids with resolutions in the order of hundred million cells. Both cold and warm initialization strategies are used to obtain Reynolds-Averaged Navier-Stokes (RANS) solutions to be used as base flows for the GSA analysis. Due to the limitations of the RANS framework, some discrepancies exist with the experiments in wing outboard region, where the RANS solutions over-predict separation. Despite the cold and warm initialization strategies converging to two different base flow solutions, GSA predicts the same unstable mode at a Strouhal number (non-dimensionalized frequencies with free-stream velocity and mean aerodynamic chord) of St approximate to 0.46. This mode corresponds to streamwise developing vortical structures that originate at the separation inside the hollow nacelle used in the wind-tunnel experiments. Once outside the nacelle, these structures are deflected upwards and impact on wing pressure side and extracted flaps, potentially contributing to oscillations in the aerodynamic forces. While in a real aircraft the nacelle will house the engine, it is important to determine the origin of unsteady phenomena that might be seen in experimental campaigns used as reference for the development and validation of numerical simulation tools.

Recent studies of the high-lift configuration of NASA's Common Research Model (CRM-HL) showed a wide spread of results using steady and unsteady 3D Reynolds-Averaged Navier-Stokes (RANS) computations at free-air conditions[1]. The possible influence of wind-tunnel wall confinement effects raises questions over the disagreement and uncertainties observed when correlating CFD results to experimental measurements. To address this question, we perform Delayed Detached-Eddy Simulations (DDES) in this work for free-air and in-tunnel conditions. While RANS solutions for free-air and in-tunnel configurations were highly sensitive to their initial conditions, free-air DDES did not exhibit such trends. However, DDES consistently underestimated lift by approximately 5% even at moderate angles of attack, where the aerodynamic loads over the flaps are high. Over-prediction of flow separation was observed at both in-board as well as out-board regions of the wing. Steady in-tunnel RANS simulations were used to assess sensitivity to boundary conditions and subsequently provide baseline settings for unsteady simulations, which were started from isentropic nozzle flow solutions. It is shown that targeted reference conditions can be obtained using different sets of boundary conditions, even though flow conditions differ in the downstream part of the test section. Unsteady in-tunnel simulations exhibited lift coefficient ranges close to experimental values. The present simulation strategy, however, led to very long initial transients before measurements could be taken on the fully developed wind-tunnel flow. In addition, it is very difficult to control the Mach number in the test section for present cold-started DDES. Overall, free-air and in-tunnel DDES deliver results of similar accuracy with respect to experiments. While frequencies corresponding to spectral peaks of lift histories agree well between free-air and in-tunnel simulations, the associated oscillation magnitudes can differ.

Recent research into buffet in the transonic flow regime has been focused on a limited number of proprietary airfoil geometries and has mainly considered parametric variations in Mach number and angle of attack. In contrast, relatively little is known about the sensitivity of buffet frequencies and amplitudes to geometric properties of airfoils. In the present contribution, an airfoil geometry construction method based on a small number of parameters is developed. The resulting airfoils and computational grids are high-order continuous everywhere except at the trailing edge corners. The effects of four key geometric parameters, defined by local extrema of coordinates on the airfoil at the design condition and denoted as 'crest' points, are studied using large-eddy simulation, considering both free-transitional and tripped boundary layers. For both states of the boundary layer, buffet amplitude and frequency are found to be highly sensitive to the axial and vertical position of the suction-side crest point, while the vertical crest position on the pressure side affects the mean lift. The present work confirms that buffet can appear for free-transitional (laminar buffet) and tripped conditions (turbulent buffet) with similar sensitivities. For test cases near onset conditions intermediate-frequency phenomena have been observed, which were linked to unsteadiness of separation bubbles. Frequencies scaling based on mean-flow properties of the separation bubble were shown to be in good agreement with previous findings on different airfoil geometries in Zauner et al. (Flow Turb. & Comb., Vol. 110, 2023, pp. 1023-1057). Airfoil geometries are provided as open source: https://doi.org/10.5281/zenodo.12204411.

Transonic buffet is an instability characterized by shock oscillations and separated boundary layers. High-fidelity simulations have typically been limited to narrow domains to be computationally feasible, overly constraining the flow and introducing modeling errors. Depending on the boundary-layer state upstream of the interaction, different buffet features are observed. High-fidelity simulations (implicit large-eddy simulation) were performed on the periodic (infinite) NASA-CRM wing at a moderate Reynolds number to assess the sensitivity of the two-dimensional transonic buffet to boundary-layer state and domain width. Simulations were cross-validated against low-fidelity Reynolds-averaged Navier–Stokes (RANS)/unsteady RANS and global stability analysis, and excellent agreement was found near the onset. By varying the boundary-layer tripping amplitude, laminar, transitional, and turbulent buffet interactions were obtained. All cases consisted of a single shock and low-frequency oscillations [Formula: see text]. The transitional interaction also exhibited reduced shock movement, a 15% increase in [Formula: see text], and energy content at higher frequencies [Formula: see text]. Spanwise domain studies showed sensitivity at the shock location and near the trailing edge. We conclude that the span width must be greater than the trailing-edge boundary-layer thickness to obtain span-independent solutions. For largely separated cases, the sensitivity to span width increased, and variations across the span were observed. This was found to be associated with a loss of two-dimensionality in the flow.

To reduce the time-to-market of future aircraft, it is crucial to predict the flight envelope accurately before building prototypes for flight tests. The High-Lift Prediction Workshop series aims to assess the numerical prediction capability of current computational fluid dynamics technology considering the high-lift version of the NASA's Common Research Model. The present work contributes to these collaborative efforts, quantifying sensitivities for Reynolds-averaged Navier-Stokes (RANS)-based steady, unsteady, and hybrid RANS/large-eddy-simulation scale-resolving approaches. Uncertainties associated with the choice of turbulence model, initialization strategies, grid resolution, and iterative convergence at free-air conditions are covered. Near stall, a large spread of RANS results was observed for different turbulence models and initialization strategies, while iterative convergence appeared less crucial for the present simulations. Steady and unsteady RANS simulations were unable to predict the correct flow physics near CL,max, even for large grids. Delayed detached-eddy simulations (DDES), however, showed good accuracy compared with wind-tunnel experiments and predicted CL,max with an error of around 5%. Compared to steady RANS, the computational cost of DDES was a factor of 10 higher. Lessons learned and potential best-practice strategies are shared to aid future studies. While warm-started RANS simulations using Spalart-Allmaras models are recommended at lower angles of attack, scale-resolving methods are required near stall.

Turbulent transonic buffet is an aerodynamic instability causing periodic oscillations of lift/drag in aerospace applications. Involving complex coupling between inviscid and viscous effects, buffet is characterised by shock-wave oscillations and flow separation/reattachment. Previous studies have identified both 2D chordwise shock-oscillation and 3D buffet/stall-cell modes. While the 2D instability has been studied extensively, investigations of 3D buffet have been limited to only low-fidelity simulations or experiments. Due to computational costs, almost all high-fidelity studies to date have been limited to narrow span-widths around 5% of aerofoil chord length (aspect ratio, $AR = 0.05$), which is insufficiently wide to observe large-scale three-dimensionality. In this work, high-fidelity simulations are performed up to $AR=3$, on infinite unswept NASA-CRM wing profiles at $Re=5\times 10^{5}$. At $AR \geq 1$, intermittent 3D separation bubbles are observed at buffet conditions. While previous RANS/stability-based studies predict simultaneous onset of 2D- and 3D-buffet, a case with buffet that remains essentially-2D despite span-widths up to $AR=2$ is identified here. Strongest three-dimensionality was observed near the low-lift phases of the buffet cycle at maximum flow separation, reverting to essentially-2D behaviour during high-lift phases. Buffet was found to become three-dimensional when extensive mean flow separation was present. At $AR \geq 2$, multiple 3D separation bubbles form, in a wavelength range of $\lambda=\left[1c-1.5c\right]$. SPOD and cross-correlations were applied to analyse the spatio/temporal structure of 3D buffet-cells. In addition to the 2D chordwise shock-oscillation mode (Strouhal number $St \approx 0.07-0.1$), 3D modal structures were found in the shocked region of the flow at $St \approx 0.002-0.004$.

To reduce the time-to-market of future aircraft, it is crucial to predict the flight envelope accurately before building prototypes for flight tests. The High-Lift Prediction Workshop (HLPW) series aims to assess the numerical prediction capability of current CFD technology considering NASA's high-lift version of the Common Research Model (CRM-HL). The present work contributes to these collaborative efforts, quantifying sensitivities for RANS-based steady, unsteady, and hybrid RANS/LES scale-resolving approaches. Uncertainties associated with the choice of turbulence model, initialization strategies, grid resolution, and iterative convergence at free-air conditions are covered. Near stall, a large spread of RANS results was observed for different turbulence models and initialization strategies, while iterative convergence appeared less crucial for the present simulations. Steady and unsteady RANS simulations were unable to predict the correct flow physics near CLmax, even for large grids. Delayed Detached Eddy Simulations (DDES), however, showed good accuracy compared with wind-tunnel experiments and predicted CLmax with an error of around 5%. Compared to steady RANS, the computational cost of DDES was a factor of ten higher. Lessons learned and potential best-practice strategies are shared to aid future studies. While warm-started RANS simulations using SA models are recommended at lower angles of attack, scale-resolving methods are required near stall.

In this paper, we develop and test an Embedded Large Eddy Simulation for predicting unsteady shockwave oscillation over an airfoil, known as transonic buffet phenomena. We implement the ELES method into our numerical solver, FaSTAR, and perform an unsteady flow simulation over an OAT15A airfoil at flow conditions of Re = 3 millions, M = 0.73, and AoA = 3.5 degrees. The numerical result shows that the ELES method is implemented correctly, and the RANS/LES switching works as expected. The result indicates that the presented method simulated the key physics of the transonic buffet phenomenon including the periodical separation/reattachment motion behind the shock. We also conducted quantitative valuation of our results by comparison with the experimental and higher-fidelity numerical data. The investigation suggested that our results are consistent with tye previous data.

Thanks to their large number of threads, GPUs allow massive parallelization, hence good performance for numerical simulations, but also make asynchronous execution more common. Kernels that do not actively take part in a computation can be executed asynchronously in the background, in the aim to saturate the GPU threads. We optimized this asynchronous execution by using mixed precision for such kernels. Implemented on the FaSTAR solver and tested on the NASA CRM case, asynchronous execution gave a speedup of 15% to 27% for a maximum memory overhead of 4.5% to 9%.

This paper investigates the flow around the tail of the NACA CRM model and its influence on aerodynamic prediction, especially for the drag/lift and moments coefficients. We examine the effects of the computational grid, turbulence models, and related numerical setups that are reported as possible factors of the large scatters on pitching moment in the first stability and control prediction workshop (SCPW1). We perform the grid convergence studies for the tail to assess the influence of the separation bubbles at the juncture section between the horizontal tail and the fuselage. We found that the finer grid size causes the separation and the pitching moment remarkably varies, depending on the occurrence of the separation bubble at the tail. The grid dependence can be eliminated by employing the quadratic constitutive relation (QCR) for the anisotropy of the Reynolds stress in a turbulent flow.

The dynamic stability of a reentry lifting capsule with a large aftbody was studied by synergistic experimental and numerical investigations. Free-to-rotate wind-tunnel tests showed that self-induced pitch oscillations depended on the Mach number, Reynolds number, and surface roughness. The experiment provided the amplitudes and frequencies of oscillations for numerical simulations in prescribed motions. Both data reduction methods for the damping coefficient are presented, and the time-series results of both methods are compared. The validated numerical simulations enabled detailed visualization of the separated flow on the side surface of the aftbody to investigate the effects of flow separation and attachment on the dynamic stability and the effect of sting interference. The dynamic characteristics observed in a postflight test with a scaled model of the recovered capsule agreed with those of the reconstructed flight in spite of deceleration effects. Wind-tunnel testing and numerical simulations as well as their mutually validated investigations provided sufficient information to fly the small lifting capsule.

This work summarizes the contribution of the Japan Aerospace Exploration Agency (JAXA) to the 7th AIAA CFD Drag Prediction Workshop (DPW7). This workshop aims at assessing the capabilities of state-of-the-art computational fluid dynamics (CFD) solvers at off-design conditions on industry relevant geometries, such as the NASA Common Research Model (CRM) wing-body configuration, for which experimental data are available from different wind tunnel facilities. Using the committee-provided 6-member family grids, Reynolds-averaged Navier-Stokes (RANS) calculations have been performed with two of JAXA’s in-house solvers, namely TAS-code and FaSTAR, for the grid convergence (case 1), angle of attack sweep (case 2) and Reynolds number sweep (case 3) studies. For the simulations at target lift-coefficient of 0.58 in case 1, the flow is fully attached on the aircraft and good grid convergence is obtained. The grid sensitivity at high angles of attack, for which large separations occur, remains to be determined. The angle of attack sweep study in case 2 shows that the quadratic constitutive relation (QCR) needs to be applied to the one-equation Spalart-Allmaras model with rotation correction (SA-R) to avoid overpredicting the side-of-body separation. The aerodynamic coefficients differ with the experimental results and need to be arbitrarily shifted to at least match the measurements at low angles of attack. This shift is intended to group all numerical and experimental uncertainties and its necessity is currently under discussion within the workshop. In case 3, when Reynolds number and dynamic pressure are changed, the correct drag trends are captured. When TAS-code and FaSTAR used the same turbulence model, remarkable agreement was achieved, and these results are consistent with those of the other DPW7 participants. The differences with the reference experiments and the difficulties in understanding their origin suggest that a more detailed characterization of the experimental setup is required in order to promote CFD progress in adequately capturing the flow physics during off-design phases of the flight envelope.

With the intent to test state-of-the-art computational methods for industry relevant geometries and flow conditions, fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. Differently from other methods present in the literature, the combination of the solver linearization approach and modal decomposition method based on time-stepper and Arnoldi iterations allows to relax the memory requirements and enables GSA investigations on fine grids and high Reynolds numbers. Based on the 7th AIAA Drag PredictionWorkshop setup, Reynolds Averaged Navier-Stokes (RANS) calculations are performed for a Reynolds number of 20 × 10^6. The RANS solutions are in reasonable good agreement with the experiments and four solution branches are identified within the angle of attack range investigated. The four branches are categorised based on the presence of separations on the main wing and on the wing-body juncture. These RANS solutions are then used to perform GSA and buffet onset is predicted at 4.30deg. Non-dimensional frequencies and a buffet cells mode are similar to those found responsible for buffet onset at wind tunnel Reynolds number conditions. At flight Reynolds numbers, the onset is however also characterised by an unstable side-of-body separation mode consisting of downstream traveling structures localised in the wing-body juncture. Despite the known limitations of RANS-based calculations, this work proves that GSA is feasible for large 3D numerical grids and high Reynolds numbers. Given the computational cost saving with respect to classical nonlinear URANS, GSA represents an additional tool to be used for buffet onset prediction during both design and certification phases of commercial aircraft.

Following on from NASA’s recent Fourth High-lift Prediction Workshop (HLPW-4), an extensive parametric study is performed for both steady and unsteady 3D Reynolds-averaged Navier-Stokes (RANS) calculations on the high-lift configuration of the NASA Common Re- search Model (CRM-HL). The sensitivity of the solution and convergence characteristics are assessed for a wide range of turbulence closure models on two grid configurations contain- ing 200 and 400 million elements. While HLPW-4 focused mostly on the use of the standard Spalart-Allmaras (SA) turbulence models, we extend the analysis in this work to assess several corrections to the standard SA model and also the more costly Shear-Stress Transport (SST) turbulence model. An overlooked issue during the HLPW-4 was the unsatisfactory convergence of the RANS solutions, that in some instances was poor even at low angles of attack. To estimate the convergence of the RANS solutions, we propose a new physics-based parameter to quantify the numerical quality and uncertainty of RANS simulation results. This parameter is shown to be more sensitive and representative of the reliability of the RANS solutions with respect to the classical L2-norm residuals. Discussions based on this parameter and the comparisons with the available experiments show that the standard SA model with quadratic constitutive relation (QCR) correction does not necessarily improve the accuracy of the results and the standard SA model should be preferred. Good aerodynamic forces predictions are obtained when warm started calculations were performed. Similar to the trends seen during HLPW-4, even though lift coefficients agree well with experiments, we however note the presence of unphysical large regions of flow separation near the wing tips for all simulations at higher angles of attack. The prediction of the pitching-moment coefficient is also unsatisfactory. For all SA-based closure models presented here, the RANS simulations were shown to be insensitive to grid refinement. While SST models perform worse than SA models at lower angles of attack, they exhibit im- proved accuracy at near-stall conditions albeit with slower convergence. Cold-started URANS simulations recover best-practice solutions of steady RANS simulations, giving confidence to the warm started RANS calculations. We also performed some preliminary global stability analyses of RANS baseflows that suggest the existence of an unstable mode associated with vor- tical structures originating from the pylon at a Strouhal number of St = 3.54 (f = 172.5Hz). More investigations are however needed to conclude on the existence of low-frequency instabil- ities associated with buffet or stall phenomena.

View Video Presentation: https://doi.org/10.2514/6.2023-1222.vid High-fidelity numerical studies of three-dimensional airfoil flows require extremely large scale computational resources. Many of the industry-relevant studies at operating flight conditions over a range of flow-speeds rely on low-fidelity RANS-based solvers to make the computational challenge tractable. In order to perform more accurate scale-resolving simulations, this work describes extensions to a high-fidelity Computational Fluid Dynamics (CFD) solver, OpenSBLI, to target transonic airfoil flows on structured meshes. OpenSBLI is an open-source code-generation system for compressible CFD on heterogeneous computing architectures. OpenSBLI generates a complete CFD solver in the Oxford Parallel Structured (OPS) domain specific language. The OPS library is embedded in C/C++, enabling massivelyparallel execution on various high-performance-computing architectures, including GPUs. As an important step to target critical phases of the flight envelope such as transonic buffet, more computationally efficient shock-capturing methods are added to the code based on a non-linear WENO filtering framework. The methods are shown to have lower numerical dissipation and reduced computational cost compared to other schemes for a supersonic Taylor-Green vortex case. Curvilinear geometries are validated for circular cylinder cases. Finally, high-fidelity airfoil simulations are presented at a Reynolds number of 500,000. A range of sharp and rounded trailing edge configurations are compared to show the effect of trailing edge treatment. The effect of spatial filtering is also shown for code-to-code comparisons of transonic buffet at moderate Reynolds numbers, with good agreement observed with respect to reference data. The present work demonstrates the suitability of code-generation methods and domain specific languages for high-fidelity aerospace research.

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier–Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft.