Parviz Moin

Abstract We present direct simulation results on turbulent spots developing spatially through a 1000 radii-long fully-developed laminar pipe flow at Re = 2150, 2300 and 2500. We seek answers to the following questions: What does an equilibrium puff do while waiting for its turn to split? Is split a sudden memoryless event or a gradual process with some unknown hysteresis effect? How is puff identity affected by such a hysteresis effect, if it does exist? Rather than waiting passively as translating frozen eddies between splits, puffs are discovered here to constantly undergo a quasi-cyclic process as manifested by a life cycle localized in their frontal elongated zone. This is accompanied by a quasi-cyclic oscillation in their front propagation speed. Spot identity may vary due to a composite process including, sequentially, multi-generational splits, reconnect, and resplits. This finding carries implications to studies on the critical Reynolds number at which turbulence starts to spread in pipe flow: Puff life-time and split waiting-time statistics may be less accurate if such spot identity variation is not tracked and included in the sampling procedure. A set of movies documenting these composite processes with remarkable clarity has been constructed.

This work studies the breakup propensity of the stratocumulus-topped boundary layer (STBL) interacting with gravity waves using large-eddy simulation with a uniform vertical grid of $5$ m and horizontal spacing of $30$ m. A radiative-convective equilibrium (RCE) state is constructed to enforce stationarity in the STBL, and the gravity waves are introduced via a vertical momentum forcing mimicking a packet of plane waves. A nondimensionalization involving the inversion height and mean horizontal base wind as length and velocity scales is proposed to provide a framework to analyze the forcing parameter space. The magnitude of the scaled forcing amplitude ($\mathcal{A}$) is critical in understanding various STBL breakup conditions. Classification of breakup was based on the reduction of the liquid water path for each forced STBL case. We found that breakup did not occur for $\mathcal{A}<1$ and observed modest reductions in cloud for $1<\mathcal{A}<2$, but the deck recovered to the stationary state slowly after the single-period forcing ceased. Fixing $\mathcal{A}\sim 2$ showed that forcings with longer duration and wider locality promote breakup. However, when the forcing is a linear combination of waves of two different periods, the percentage of cleared cloud dramatically increases, though recovery of RCE is still observed in some cases. $\mathcal{A}\geq2.5$ marks a critical threshold by which the STBL breaks up entirely and remains patchy. We further explore the connection between these bulk breakup results and the turbulent state by examining energy budgets and the anisotropy induced by the forcing.

This work studies the breakup propensity of the stratocumulus-topped boundary layer (STBL) interacting with gravity waves using large-eddy simulation with a uniform vertical grid of $5$ m and horizontal spacing of $30$ m. A radiative-convective equilibrium (RCE) state is constructed to enforce stationarity in the STBL, and the gravity waves are introduced via a vertical momentum forcing mimicking a packet of plane waves. A nondimensionalization involving the inversion height and mean horizontal base wind as length and velocity scales is proposed to provide a framework to analyze the forcing parameter space. The magnitude of the scaled forcing amplitude ($\mathcal{A}$) is critical in understanding various STBL breakup conditions. Classification of breakup was based on the reduction of the liquid water path for each forced STBL case. We found that breakup did not occur for $\mathcal{A}<1$ and observed modest reductions in cloud for $1<\mathcal{A}<2$, but the deck recovered to the stationary state slowly after the single-period forcing ceased. Fixing $\mathcal{A}\sim 2$ showed that forcings with longer duration and wider locality promote breakup. However, when the forcing is a linear combination of waves of two different periods, the percentage of cleared cloud dramatically increases, though recovery of RCE is still observed in some cases. $\mathcal{A}\geq2.5$ marks a critical threshold by which the STBL breaks up entirely and remains patchy. We further explore the connection between these bulk breakup results and the turbulent state by examining energy budgets and the anisotropy induced by the forcing.

This article aims to present preliminary aeroelastic simulation results of the NASA Benchmark Supercritical Wing (BSCW) with wall-modeled large-eddy simulations (WMLES) paradigm and moving meshes. A series of direct numerical simulations (DNS) of forced-oscillation and free flutter of the NACA0012 airfoil at $Re_\infty=10,000$ was performed, and the results are compared to reference literature as solver validations. The cases selected for the BSCW configuration are from the AIAA Aeroelastic Prediction Workshop (AePW), and this article presents WMLES results of the forced-oscillation case at attached flow condition (Case \#1 \nth{2} AePW) and the transonic shock-buffet case with shock-induced flow separations (Case \#2, \nth{3} AePW). The pressure coefficient $C_p$ on the upper surface at span $y/b=0.6$ and the frequency response functions of $C_p$ against the pitching angle are computed for the forced-oscillation case, and the results show excellent agreement with reference experimental results. The surface $C_p$ and its statistics are computed for the shock-buffet case. Reasonable agreement with experimental data is observed in the simulations.

This work presents a high-fidelity, multi-physics framework for investigating the heat transfer of aircraft icing under realistic conditions. The methodology integrates a compressible Wall-Modeled Large-Eddy Simulation (WMLES) solver for aerodynamics, a Lagrangian particle tracking method for droplet impingement, and an unsteady Conjugate Heat Transfer (CHT) solver for the solid ice domain. This framework is applied to a NACA 23012 airfoil featuring laser-scanned rime ice roughness to analyze the interplay between surface topology, droplet impingement, and thermal conduction driven by the solidification of supercooled droplets. Results reveal that surface roughness induces high-frequency spatial variations in the local collection efficiency, leading to a heterogeneous heat source distribution from droplet solidification. However, lateral conduction within the ice layer diffuses this localized heat generation, resulting in a surface temperature field that is notably smoother than the impingement profile. Analysis of the interfacial energy budget at the stagnation region indicates that approximately 30\% of the latent heat released by droplet freezing is conducted into the ice layer. Temperature profiles within the solid reveal that near the inner airfoil skin, the conduction is mostly one-dimensional. However, near the highly irregular ice surface, the three-dimensional nature of the roughness elements drives multi-dimensional conduction, redirecting heat laterally from warm windward faces to cool leeward regions of individual roughness elements. These findings suggest that traditional icing models relying on isothermal wall assumptions or simplified one-dimensional conduction may not adequately capture the local thermodynamics of rough ice accretions.

This work presents a non-mixture approach based on the ghost-fluid method (GFM) for simulating compressible multiphase flows with the goal of achieving enhanced accuracy and efficiency on coarse computational meshes. Building upon the classical GFM approach, a narrow-band level-set method is developed by introducing a modified Hamilton-Jacobi equation. The method has demonstrated fast convergence during the reinitialization process and preserves the interface geometry by imposing essential numerical conditions. The numerical implementation details and initial validation results demonstrate the effectiveness of the proposed enhancements in capturing complex interfacial phenomena.

Accurate heat transfer prediction on rough surfaces is critical for ice accretion prediction and aviation safety. Using high-fidelity simulations of conjugate heat transfer, we resolve heat transport in both the fluid and a low-conductivity solid featuring laser-scanned ice roughness. Contrary to the behavior of isothermal surfaces, the low thermal conductivity of the solid causes roughness crests to become the coolest points, sometimes even drawing heat from the air. This work highlights the necessity of including solid conduction effects in next-generation icing models.

Turbulence–chemistry interaction in a Mach-7 hypersonic boundary layer with significant production of radical species is characterised using direct numerical simulation. Overriding a non-catalytic surface maintained as isothermal at 3000 K, the boundary layer is subject to finite-rate chemical effects, comprising both dissociation/recombination processes as well as the production of nitric oxide as mediated by the Zel’dovich mechanism. With kinetic-energy dissipation giving rise to temperatures exceeding 5300 K, molecular oxygen is almost entirely depleted within the aerodynamic heating layer, producing significant densities of atomic oxygen and nitric oxide. Owing to the coupling between turbulence-induced thermodynamic fluctuations and the chemical-kinetic processes, the Reynolds-averaged production rates ultimately depart significantly from their mean-field approximations. To better characterise this turbulence–chemistry interaction, which arises primarily from the exchange reactions in the Zel’dovich mechanism, a decomposition for the mean distortion of finite-rate chemical processes with respect to thermodynamic fluctuations is presented. Both thermal and partial-density fluctuations, as well as the impact of their statistical co-moments, are shown to contribute significantly to the net chemical production rate of each species. Dissociation/recombination processes are confirmed to be primarily affected by temperature fluctuations alone, which yield an augmentation of the molecular dissociation rates and reduction of the recombination layer’s off-wall extent. While the effect of pressure perturbations proves largely negligible for the mean chemical production rates, fluctuations in the species mass fractions are shown to be the primary source of turbulence–chemistry interaction for the second Zel’dovich reaction, significantly modulating the production of all major species apart from molecular nitrogen.

This work examines the flow separation and the resulting pressure distortions at the exit plane of a serpentine diffuser operating at both subsonic and transonic conditions. Wall modeled large-eddy simulations (WMLES) using the charLES flow solver are performed at three exit-plane Mach numbers, Ma_AIP ≈ {0.36, 0.46, 0.54}. First, it is shown that the onset of flow separation inside a serpentine diffuser may likely experience strong, non-local history effects. A grid refinement study consisting of five grids (from 30 million to 3 billion cells) is conducted for all Mach numbers. The recently proposed dynamic tensor-coefficient Smagorinsky subgrid-scale and sensor-aided non-equilibrium wall models compare favorably with experimental measurements for the pressure recovery and azimuthal flow distortion at all Mach numbers. The pressure recovery and azimuthal flow distortion are predicted to within 0.3% and 7%, respectively, which are both within the experimental error bounds. However, the simulations underpredict the maximum azimuthal distortion in comparison to the experiments for all conditions. Statistical comparisons of the dynamic azimuthal flow distortions suggest that the present LES reasonably captures the ring-averaged mean distortions, and the statistical distributions of the distortion around the mean. Extreme events are underestimated by the present simulations, potentially highlighting that significantly longer integration times may be necessary.

This work examines the flow separation and the resulting pressure distortions at the exit plane of a serpentine diffuser operating at both subsonic and transonic conditions. Wallmodeled large-eddy simulations (WMLES) using the charLES flow solver are performed at three exit-plane Mach numbers, Ma_AIP ~ {0.36, 0.46, 0.54}. First, it is shown that the onset of flow separation inside a serpentine diffuser may likely experience strong, non-local history effects. A grid refinement study consisting of five grids (from 30 million to 3 billion cells) is conducted for all Mach numbers. The recently proposed dynamic tensor-coefficient Smagorinsky subgrid-scale and sensor-aided non-equilibrium wall models compare favorably with experimental measurements for the pressure recovery and azimuthal flow distortion at all Mach numbers. The pressure recovery and azimuthal flow distortion are predicted to within 0.3% and 7%, respectively, which are both within the experimental error bounds. However, the simulations underpredict the maximum azimuthal distortion in comparison to the experiments for all conditions. Statistical comparisons of the dynamic azimuthal flow distortions suggest that the present LES reasonably captures the ring-averaged mean distortions, and the statistical distributions of the distortion around the mean. Extreme events are underestimated by the present simulations, potentially highlighting that significantly longer integration times may be necessary.

Large-eddy simulations (LES) are used to investigate the aerodynamic performance of a semispan swept-wing model based on the NASA Common Research Model. Two ice shapes are considered: 1) a real ice shape from laser-scanning accreted ice in the NASA Icing Research Tunnel and 2) an artificial ice shape derived from the maximum combined cross-section of the 3D ice accretion. Simulations are performed in free air at Reynolds numbers, [Formula: see text], of [Formula: see text], [Formula: see text], and [Formula: see text], with a Mach number of 0.18. Integrated loads, pressure distributions, and wall-shear stress visualizations are compared to experiments over various angles of attack. Grid resolution studies show good agreement for the real ice geometry, with lift coefficient differences within three counts ([Formula: see text]). The artificial ice geometry, however, shows greater sensitivity to grid resolution. Despite good agreement in lift for the artificial ice shape, discrepancies in drag and moments are observed. Pressure profiles suggest error cancellation, explaining the lift agreement. The smooth surfaces in the artificial ice shape introduce laminar boundary layers, laminar separation, and turbulent transition, unlike real ice, where roughness triggers immediate transition. These findings highlight the importance of incorporating appropriate roughness scales into artificial or predicted ice shapes for practical LES in iced aircraft configurations.

This paper utilizes the large-eddy simulation (LES) paradigm with a physics-based turbulence modeling approach, including a dynamic subgrid-scale model and an equilibrium wall model, to examine the flow over the NASA transonic Common Research Model (CRM), a flow configuration that has been the focus of several AIAA Drag Prediction Workshops (DPWs). The current work explores sensitivities to laminar-to-turbulent transition, wind tunnel mounting system, grid resolution, and grid topology and makes suggestions for current best practices in the context of LESs of transonic aircraft flows. It is found that promoting the flow transition to turbulence via an array of cylindrical trip dots, including the sting mounting system, and leveraging stranded boundary-layer grids all tend to improve the quality of the LES solutions. Non-monotonic grid convergence in the LES calculations is observed to be strongly sensitive to grid topology, with stranded meshes rectifying this issue relative to their hexagonal close-packed counterparts. The details of the boundary-layer profiles, both at the leading edge of the wing and within the shock-induced separation bubble, are studied, with thicknesses and integral measures reported, providing details about the boundary-layer characteristics to turbulence modelers not typically available from complex aircraft flows. Finally, an assessment of the initial buffet prediction capabilities of LES is made in the context of a simpler NACA 0012 flow, with computational predictions showing reasonable agreement with available experimental data for the angle of attack at initial buffet onset and shock oscillation frequency associated with sustained buffet.

This work applies the non-equilibrium wall model of Agrawal et al., 2024 (arXiv preprint, arXiv:2407.11390) to the flow over the QinetiQ High-Lift Common Research Model aircraft at low angles of attack. This choice is motivated by the previously reported misprediction of flow separation on the trailing edges of the flap in wall-modeled large-eddy simulations of this aircraft. It is shown that the proposed non-equilibrium model identifies conditions where the boundary layer significantly departs from equilibrium conditions around the trailing edges of the flap and the wing-body fairing. Further, the model provides improved predictions of the integrated loads, such as the lift, pitching moment, and drag in this regime for two grids containing 103 and 384 million control volumes, respectively, relative to the equilibrium wall model. The surface pressure data suggests the overprediction of lift from the equilibrium wall model is correlated with an overproduction of the suction peak and the reduced ���� flattening around the flaps. Finally, it is also shown that the refinement of the fuselage boundary layer and the uniformity of the grid distribution on the wing elements can further improve the predictions of flap separation.

Wall-modeled large-eddy simulations (WMLES) are conducted of the flow over a semi-span, NASA High-Lift Common Research Model (CRM-HL) mounted on the side-wall of the NTF wind tunnel at two mean-aerodynamic-chord-based Reynolds numbers: Re = 5.5 × 10^6 and 30 × 10^6. This study is performed as a blind test of the predictive capabilities of WMLES for integrated aerodynamic loads (lift, drag, and pitching moment) as the Reynolds number increases, as well as an assessment of predicted wind-tunnel effects in comparison to the recent free-air investigations of Agrawal et al., AIAA Aviation, 2024. In the lower angle of attack regime, the lift is increased (with a lowered drag) relative to the free-air values, equivalent to an angle (1 deg.) shift of approximately 1 deg. between the free-air and wind-tunnel predictions. An earlier stall (by 2 - 3 deg.) is observed when the aircraft model is mounted inside the tunnel at both Reynolds numbers. Although the NTF wind tunnel has pressure-relieving slots in the test section, we find that these only partially eliminate the blockage. Limited sensitivity of the predicted integrated loads to the resolution of the wind tunnel boundary layers and the treatment of the tunnel slots is demonstrated. Upon comparing the surface streamlines at both Reynolds numbers, we find that the flap separation patterns in the linear regime are consistent between free-air and in-tunnel configurations. Further, the surface streamline patterns at aerodynamic stall are qualitatively similar between free-air and in-tunnel configurations, when accounting for the earlier stall in the tunnel.

We propose a nonequilibrium wall model for improving the predictions of flow separation in complex, turbulent boundary layers. Improved predictability of smooth body separation at multiple Reynolds and Mach numbers in flows over the NASA/Boeing speed bump and the Bachalo-Johnson bumps is demonstrated at resolutions where the equilibrium model fails to separate. Scaling arguments, followed by $a$ $p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i$ verification suggest a weaker scaling of the required resolutions to capture flow separation using the proposed model compared to standard equilibrium closures.

This succinct introduction to the fundamental physical principles of turbulence provides a modern perspective through statistical theory, experiments, and high-fidelity numerical simulations. It describes classical concepts of turbulence and offers new computational perspectives on their interpretation based on numerical simulation databases, introducing students to phenomena at a wide range of scales. Unique, practical, multi-part physics-based exercises use realistic data of canonical turbulent flows developed by the Stanford Center for Turbulence Research to equip students with hands-on experience with practical and predictive analysis tools. Over 20 case studies spanning real-world settings such as wind farms and airplanes, color illustrations, and color-coded pedagogy support student learning. Accompanied by downloadable datasets, and solutions for instructors, this is the ideal introduction for students in aerospace, civil, environmental, and mechanical engineering and the physical sciences studying a graduate-level one-semester course on turbulence, advanced fluid mechanics, and turbulence simulation.

This paper proposes a Reynolds number [Formula: see text] scaling for the number of grid points [Formula: see text] required in wall-modeled Large Eddy Simulation (WMLES) of turbulent boundary layers (TBL) to accurately capture the regions of flow separation. Based on the various time scales in a nonequilibrium TBL, a definition of the near-wall “underequilibrium” scales is proposed (in which “equilibrium” refers to a quasi balance between the viscous and the pressure gradient terms). This length scale is shown to vary with Reynolds number as [Formula: see text]. A-priori analysis demonstrates that the resolution ([Formula: see text]) required to reasonably predict the wall stress in several nonequilibrium flows is at least [Formula: see text], irrespective of the Reynolds number and Clauser parameter. Further, a-posteriori studies (on the Boeing speed bump, Song– Eaton diffuser, Notre-Dame Ramp, and the backward-facing step) show that scaling [Formula: see text] such that [Formula: see text] is independent of Reynolds number results in accurate predictions of separation for the same “nominal” grid across different Reynolds numbers. Finally, we suggest that near separation and reattachment points, [Formula: see text] for WMLES scale as [Formula: see text], which is more restrictive than the previous estimates ([Formula: see text]) by Choi and Moin (Choi, H., and Moin, P., “Grid-Point Requirements for Large Eddy Simulation: Chapman’s Estimates Revisited,” Physics of Fluids, Vol. 24, No. 1, 2012, Paper 011702) and Yang and Griffin (Yang, X. I. A., and Griffin, K. P., “Grid-Point and Time-Step Requirements for Direct Numerical Simulation and Large-Eddy Simulation,” Physics of Fluids, Vol. 33, No. 1, 2021, Paper 015108).

Accurate modeling of ice accretion is important for the safe and efficient design of aircraft and propulsion systems. The first step in calculating the volumes of ice accumulated on aircraft wings is to estimate the impingement rate of droplets on the lifting surfaces. When these droplets exceed diameters of 40 ��m, the splashing effects become relevant in the calculation of the collection efficiency. In this work, we present large-eddy simulations (LES) of supercooled large droplets (SLD) impingement rates using a Lagrangian particle approach. This technique is used to represent droplet clouds with and without the presence of SLDs. Best practices to accelerate the convergence rate of the collection efficiency using LES and lagrangian particles are presented. It is shown that simulating droplet clouds with significant variations in droplet sizes leads to a very slow time convergence of the collection efficiency distribution. Calculating the collection efficiency using a combination of monodisperse cloud simulations leads to a 7-fold reduction in computation time as opposed to using a single polydisperse cloud simulation. Splashing models are evaluated to assess their accuracy within the LES framework. The results presented in this article demonstrate that LES coupled with Lagrangian particle tracking is highly effective in accurately modeling the impingement rate of droplets on aerodynamic surfaces.

Wall-modeled large-eddy simulations (WMLES) are conducted of the flow over the NASA High-Lift Common Research Model (CRM-HL) in free-air configuration for a set of mean aerodynamic-chord Reynolds numbers: Re_MAC =5.5 × 10^6, 16 × 10^6, 30 × 10^6. This study is performed as a blind test of prediction capabilities for integrated forces and moments (lift, drag, and pitching moment) as the Reynolds number increases. It is observed that, as the Reynolds number increases, the grid requirements for WMLES increase non-uniformly between the low and high angles of attack. For the low angles of attack, the difficult-to-predict flap separations, present at Re_MAC = 5.5 × 106, are diminished, especially in the inboard region at higher Reynolds numbers. For the high angles of attack, similar stall mechanisms are observed across Reynolds numbers. The angle of attack at which maximum lift occurs is nearly insensitive to the Reynolds number; however, the maximum lift coefficient increases with the Reynolds number. The resolution required to converge the maximum lift condition is found to be weakly sensitive to the Reynolds number. The sensitivity of the integrated loads to the choice of a semi-span versus a full-span model is found to be minimal across the angle-of-attack sweep.

For a turbulent rough-wall flow, it is known that the outer layer of a turbulent boundary layer is independent of wall roughness effects except in the roughness's role in setting both the friction velocity and boundary layer thickness (Jimenez, 2004; Kadivar et al., 2021). To accurately model these effects, we leverage a recently developed parameterized velocity transformation for rough-wall boundary layers (Bornhoft et al., 2023). This transformation is utilized to develop a new wall model for marginally resolved rough surfaces, modifying the equilibrium wall model (EQWM). The new wall model is validated in a turbulent channel flow and compared against available DNS data, as well as on an early-time rime ice geometry against both experimental and wall-resolved LES data. In both cases, significant improvements are observed in local quantities such as velocity profiles, boundary layer growth, and local friction coefficients, as well as in integrated quantities such as lift and drag.

In this work, a non-equilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity (u_tau) and the viscous-pressure gradient velocity (up). In regions where the pressure gradient velocity is comparable to the friction velocity (up \sim u_tau, the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA-Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model can capture the onset of boundary layer separation observed in experiments or DNS calculations at resolutions where the equilibrium wall model fails to separate.

This article utilizes the Large-Eddy Simulation (LES) paradigm with a physics-based turbulence modeling approach, including a dynamic subgrid-scale model and an equilibrium wall model, to examine the flow over the NASA transonic Common Research Model (CRM), a flow configuration that has been the focus of several AIAA Drag PredictionWorkshops (DPWs). The current work explores sensitivities to laminar-to-turbulent transition, wind tunnel mounting system, grid resolution, and grid topology and suggests current best practices in the context of large-eddy simulations of transonic aircraft flows. It is found that promoting the flow transition to turbulence via an array of cylindrical trip dots, including the sting mounting system in the simulations, and leveraging stranded boundary layer grids all tend to improve the quality of the LES solutions. Non-monotonic grid convergence in the LES calculations is observed to be strongly sensitive to grid topology, and stranded meshes rectify this issue relative to their hexagonal close-packed (HCP) counterparts. The details of the boundary layer profiles both at the leading edge of the wing and within the shock-induced separation bubble are studied, with thicknesses and integral measures reported, providing details about the boundary layer characteristics to turbulence modelers not typically available from complex aircraft flows. Finally, an assessment of the initial buffet prediction capabilities of LES is made in the context of a simpler NACA 0012 flow, with computational predictions showing reasonable agreement with available experimental data for the angle of attack at initial buffet onset and shock oscillation frequency associated with sustained buffet.

Abstract This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at Re τ ≈ 180, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately 2.83 times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately 2.21 times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately 2.17 slower in the MFU than the FC.

The present study builds on prior work by taking advantage of the novel framework proposed by Griffin et al. (hereafter referred to as the GFM) as a baseline. The model is progressively extended to multicomponent reacting mixtures, accounting for differential diffusion and finite-rate chemistry in a similar fashion to Di Renzo & Urzay and Di Renzo et al. The accuracy of the present approach, as well the prior model of Di Renzo & Urzay, is assessed in an a priori sense for the first time in a turbulent reacting boundary layer, using the boundary-layer data of Williams et al. Five species are included in the present analysis, i.e., Ns = 5, namely N2, O2, NO, N and O, a neutral mixture most representative of dissociation/recombination phenomena for temperatures below 6000 K. A schematic of a flow over a wedge representative of the described configuration is presented in Figure 1. The brief is organized as follows: In Section 2, the wall-model equations and the computational framework are presented. In Section 3, the a priori results of the proposed model are described and compared to the extended EWM. Finally, in Section 4, some conclusions are offered.

A localized artificial-diffusivity method is developed for capturing discontinuities, such as shocks and contacts, in compressible flows. A new sensor for contact discontinuity makes the method more localized, and a discretely consistent formulation eliminates the need for filtering the solution or filtering the sensors to obtain robust solutions. Improved predictions are observed in canonical shock-tube problems and large-eddy simulations of homogeneous isotropic turbulence.

In this study, five ice shapes generated at NASA Glenn's Icing Research Tunnel (IRT) are simulated at multiple angles of attack (Broeren et al., J. of Aircraft, 2018). These geometries target different icing environments, both early-time and longer-duration glaze and rime ice exposure events, including a geometry that results from using a thermal ice-protection system. Using the laser-scanned geometries, detailed representations of the three-dimensional ice geometries are resolved on the grid and simulated using wall-modeled LES. Integrated loads (lift, drag, and moment coefficients) and pressure distributions are compared against experimental measurements in both clean and iced conditions for several angles of attack in both pre-and post-stall regions. The relevant comparisons to the experimental results show that qualitative and acceptable quantitative agreement with the data is observed across all geometries. Glaze ice formations exhibit larger and highly nonuniform ice features, such as `horns', in contrast to rime ice formations characterized by smaller, uniformly distributed roughness elements. In wall-modeled LES, it was observed that larger roughness scales in the glaze ice that trigger transition can be accurately resolved. Therefore, it is possible for WMLES to accurately capture the aerodynamics of glaze ice shapes without the need for additional modeling. In contrast, rime ice geometries required additional resolution to accurately represent the aerodynamic loads. This study demonstrates the effectiveness of the wall-modeled LES technique in simulating the complex aerodynamic effects of iced airfoils, providing valuable insights for aircraft design in icing environments and highlighting the importance of accurately representing ice geometries and roughness scales in simulations.

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This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at $Re_τ\approx 180$, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately $2.83$ times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately $2.21$ times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately $2.17$ slower in the MFU than the FC.

In this study, we employ wall-modeled large-eddy simulations (WMLES) to analyze the aerodynamic performance of an 8.9%-scaled semi-span swept wing model based on the NASA Common Research Model (CRM). The simulations consider two ice shapes: (1) a real-ice shape obtained from laser-scanning accreted ice in the NASA Icing Research Tunnel (IRT), and (2) a processed artificial-ice shape derived by constructing the maximum combined cross-section of the 3D ice accretion. Both ice shapes are simulated in a free-air configuration at a mean aerodynamic chord-based Reynolds number, Re_MAC, of 1.6x10^6 and Mach number of 0.18. Integrated loads (lift, drag, and moment coefficients), pressure distributions, and wall-shear stress visualizations are compared against experimental measurements for several angles of attack in both pre- and post-stall regions. The simulations are conducted at three different grid resolutions: 24 million control volumes (CV), 85 million CV, and 320 million CV. We observe good agreement across all cases for the real-ice geometry for both integrated loads and pressure distributions. The lift coefficient results closely match the experimental data, with differences within three lift counts (∆C_L=0.03) across all grid resolutions. However, the artificial-ice geometry displays greater sensitivity to grid resolution. Specifically, while the lift coefficient aligns well with the artificial-ice shape, disparities with the experimental data are observed in drag and moments. A closer examination through pressure profiles reveals that the apparent agreement in lift results from error cancellation. Introducing smooth surfaces in the artificial ice shape introduces physics not present in real ice flows, such as laminar boundary layers, laminar separation, and turbulent transition. These issues do not exist for the real ice geometry, as the roughness on the leading edge of the ice triggers bypass transition. For the artificial ice geometry, we run an additional grid resolution where we model the smooth leading edge ice shape with a no-slip condition, resulting in a grid with 1.5 billion CVs. This modification yields good agreement when comparing integrated loads and pressure profiles. This work underscores the challenges of modeling artificial ice shapes using state-of-the-art simulation approaches. We emphasize the importance of incorporating appropriate roughness scales into artificial or predicted ice shapes to ensure practical computational costs for the application of WMLES in iced aircraft configurations.

Wall-modeled large-eddy simulation (WMLES) is increasingly used as a tool for analysis of external aerodynamic applications. It has been observed that traditional wall models, which are typically based on Reynolds-averaged Navier-Stokes closures, can under-perform in flows with mild, adverse pressure gradients that result in boundary layer separation. Slip wall models are presented as an alternative formulation to predict high Reynolds number boundary layers undergoing separation. Prior studies utilizing slip wall models have shown sensitivity of results to the choices of slip length in attached boundary layers. The slip wall model is applied to a canonical case of smooth-body separation, the Boeing speed bump, and, subsequently, to the JAXA Standard Model at a low angle of attack. Significant errors in skin friction predictions are observed at coarse resolutions, particularly in regions of zero or favorable pressure gradients when using a slip length based on Prandtl mixing lengths. However, under specific choices of slip lengths, improved predictions for the JAXA Standard Model are obtained due to improved predictions of flap separation compared with the equilibrium wall model. This suggests that more robust separation predictions may be possible if a more accurate method for computing slip lengths could be developed.

Thwaites ( Aeronaut. Q. , vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971 ). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

This article proposes a Reynolds number scaling of the required grid points to perform wall-modeled LES of turbulent flows encountering separation off a solid surface. Based on comparisons between the various time scales in a non-equilibrium (due to the action of an external pressure gradient) turbulent boundary layer, a simple definition of the near-wall ``under-equilibrium" and ``out-of-equilibrium" scales is put forward (where ``under-equilibrium" refers to scales governed by a quasi-balance between the viscous and the pressure gradient terms). It is shown that the former length scale varies with Reynolds number as lp Re^(-2/3). The same scaling is obtained from a simplified Green's function solution of the Poisson equation in the vicinity of the separation point. A-priori analysis demonstrates that the resolution required to reasonably predict the wall-shear stress (for example, errors lower than approximately 10-15% in the entire domain) in several nonequilibrium flows is at least O(10) lp irrespective of the Reynolds number and the Clauser parameter. Further, a series of a-posteriori validation studies are performed to determine the accuracy of this scaling including the flow over the Boeing speed bump, Song-Eaton diffuser, Notre-Dame Ramp, and the backward-facing step. The results suggest that for these flows, scaling the computational grids () such that / lp is independent of the Reynolds number results in accurate predictions of flow separation at the same ``nominal" grid resolution across different Reynolds numbers. Finally, it is suggested that in the vicinity of the separation and reattachment points, the grid-point requirements for wall-modeled large eddy simulations may scale as Re^4/3, which is more restrictive than the previously proposed flat-plate boundary layer-based estimates (Re1) of Choi and Moin (Phys. Fluids, 2012) and Yang and Griffin (Phys. Fluids, 2021).

Thwaites (1949) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of a flow parameter, $m = θ^2/ν\frac{dU_e}{ds}$, thus reducing the von Karman momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. However, for turbulent flows, a similar approximation for turbulent boundary layers subjected to pressure gradients does not yet exist. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed. It is shown that the method provides good estimates of the momentum thickness, when compared to available high-fidelity simulation data, for multiple boundary layers including both favorable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model which is shown to be in agreement with prior empirical observations (Alber, \textit{$9^{th}$ Aerospace Sciences Meeting, 1971}). The sensitivity of the separation location with respect to upstream perturbations is also analyzed through this model for the NASA/Boeing speed bump and the transonic Bachalo-Johnson bump

This paper describes the application of a compressible large-eddy simulation (LES) solver to the flow over the High-Lift Common Research Model (CRM-HL) in landing configuration, a complex external aerodynamic flow configuration with deployed slats, flaps, a flow-through nacelle, and the associated brackets/fairings on the high-lift devices. The bulk Mach number is (0.2) and the mean-aerodynamic-chord-based Reynolds number is typical of a wind tunnel experiment ([Formula: see text]). A key development in these simulations relative to previous work is that this work serves to establish robustness of LES methods to Reynolds number and aircraft configuration. Previous studies focused on the Japan Aerospace Exploration Agency Standard Model, which featured a nearly [Formula: see text] lower Reynolds number than the present CRM-HL investigation and less aggressive wing/slat leading-edge curvature than the CRM-HL geometry, which led to lower leading-edge pressure suction peak magnitudes, both of which led to less stringent grid resolution requirements. In these LES simulations, an algebraic equilibrium wall modeling approach is employed along with a dynamic implementation of the Smagorinsky subgrid-scale model. The calculations are carried out in both a free air setting and one that includes the wind tunnel facility at seven angles of attack at five grid resolution levels, ranging from [Formula: see text] million control volumes. In free air, the solutions show decreasing sensitivity to the grid with each successive refinement level and systematically approach the experimental lift coefficient data as the grid is refined, with the 1.5 billion control volume case showing excellent agreement with the corrected experimental data. The simulations in both free air and in the wind tunnel predict a stall mechanism featuring a large inboard juncture stall and a nose-down break in the pitching moment curve, both of which agree with the experimental observations. The accuracy of the simulations is assessed via comparisons of integrated forces/moments, surface pressures, and surface skin friction visualizations. Graphics processing unit (GPU) acceleration of the charLES solver results in tractable turnaround times that make LES a useful tool in the aerospace industry design cycle. Recent GPU acceleration of the flow solver has made LES solutions that are highly accurate in lift/drag/moment for relevant high-lift aircraft flows achievable within about 5 h of wall time on 600 GPU cores.

In this study, five ice shapes generated at NASA Glenn's Icing Research Tunnel (IRT) are simulated at multiple angles of attack (Broeren et al., J. of Aircraft, 2018). These geometries target different icing environments, both early-time and longer-duration glaze and rime ice exposure events, including a geometry that results from using a thermal ice-protection system. Using the laser-scanned geometries, detailed representations of the three-dimensional ice geometries are resolved on the grid and simulated using wall-modeled LES. Integrated loads (lift, drag, and moment coefficients) and pressure distributions are compared against experimental measurements in both clean and iced conditions for several angles of attack in both pre-and post-stall regions. The relevant comparisons to the experimental results show that qualitative and acceptable quantitative agreement with the data is observed across all geometries. Glaze ice formations exhibit larger and highly nonuniform ice features, such as `horns', in contrast to rime ice formations characterized by smaller, uniformly distributed roughness elements. In wall-modeled LES, it was observed that larger roughness scales in the glaze ice that trigger transition can be accurately resolved. Therefore, it is possible for WMLES to accurately capture the aerodynamics of glaze ice shapes without the need for additional modeling. In contrast, rime ice geometries required additional resolution to accurately represent the aerodynamic loads. This study demonstrates the effectiveness of the wall-modeled LES technique in simulating the complex aerodynamic effects of iced airfoils, providing valuable insights for aircraft design in icing environments and highlighting the importance of accurately representing ice geometries and roughness scales in simulations.

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al. , Proc. Natl Acad. Sci. , vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.