Article

Temporal convergence criteria for time-accurate viscous simulations of separated flows

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

Airfoils and wings undergoing static and dynamic stall still elude accurate simulation by computational methods. While significant emphasis has been placed on the quantification of grid dependence, as well as influence of the turbulence method, many elements defining temporal convergence remain ad hoc. To address this, convergence and accuracy for two different turbulence methods were examined for both static and dynamic stall. New approaches to define numerical convergence that include an assessment of the physical accuracy have been developed and evaluated via a blind analysis at other stall conditions. A key finding is the need to ensure that the combination of time step and subiterations achieves a true second order accurate solution. It was also observed that accurate prediction of separation was controlled primarily by the turbulent transport terms, while the mean flow equations influenced reattachment. Temporal convergence of dynamic stall can be quantitatively assessed by an approach developed in this effort.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... Initial studies solved the URANS form of these equations with one-or two-equation turbulence models. To reduce the computational complexity, the equations were reduced to the 2-D form to study isolated 2-D pitching airfoils [5][6][7]. Flow variations in the depth (span) direction were not modeled. Over the years, studies have shown that while the 2-D flow assumption is adequate for the attached flow regime, 3-D modeling is necessary to capture the spanwise flow variation that are inherent in stalled flows. ...
... The previous 2-D studies [5][6][7] established a credible numerical model that addressed issues such as temporal resolution, spatial resolution, numerical convergence, and turbulence modeling. In Ref. 5, a grid refinement study on a NACA0015 airfoil near static stall revealed large sensitivity. ...
... The overset grids for the OA209 wing and the wind tunnel are shown in Fig. 2. Most of the grid spacing parameters were drawn from the previous experience in 2-D dynamic stall simulations [6,7]. The parameters are listed in Table 2. ...
... During the last two decades, significant improvements were made in the prediction of dynamic stall on two-dimensional rigid airfoils using Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) methods, and improved agreement with experiment can be found in the literature. [6][7][8][9][10][11][12][13] Recent work undertakes the extension of computations to three-dimensional dynamic stall. 14-16 Similar efforts have been applied to classic flutter (for example, Refs. ...
... Comparisons are made with experimental results as well as with solutions obtained using the OV ERF LOW solver. 13 At low angles of attack, as the flow is steady and the turbulence effects are negligible, so that a good agreement is found between the fsiFoam results and the other data. As the angle of attack is increased, discrepancies between the data become more significant. ...
... The results obtained are compared on Fig. 9 with numerical solutions obtained with the OVERFLOW solver, which has already been validated for similar applications. 13 It can be seen that a very good agreement is obtained for the pressure distribution data and both the stagnation point and the trailing edge region is well captured by fsiFoam. Unlike the static case, the pressure distribution recorded when the airfoil passes through α = 0 • is not symmetrical on the pressure and the suction sides of the airfoil, resulting in lift and drag aerodynamic coefficients that are similar but not coincident. ...
Conference Paper
A solver has been developed within the OpenFoam framework to compute large ampli-tude motion of two-dimensional rigid conffigurations. The results obtained with this code were successfully validated on rigid airfoils at static and dynamic conditions, as well as cor-related with experimental data and numerical solutions from similar unsteady solvers. The results demonstrate that current computational methods are, within the constraints im-posed by spatial grids, temporal integration and turbulence modeling, capable of capturing the self-sustained oscillations characterizing stall utter event with reasonable accuracy, including the mechanisms of energy transfer. Copyright © 2012 by Sacha Yabili, Marilyn J. Smith and Grigorios Dimitriadis.
... Computational predictions of static and dynamic stall have improved over the past decade due to the increased speed and accessibility of computational hardware, in concert with the development of improved transition and turbulence methods. Researchers, including Smith et al., [12][13][14] Sanchez-Rocha, 15,16 Gleize et al., 17 and Szydlowski and Costes 18 have studied stall and post-stall characteristics of static airfoils with unsteady Reynolds Averaged Navier-Stokes (URANS) computational fluid dynamics (CFD). They have examined the influence of grid dependence, spatial algorithms, and temporal integration, as well as turbulence modeling effects. ...
... The influence of turbulence modeling on unsteady airfoils including separation and reattachment has been studied by a number of researchers. 14,19 For two-dimensional simulations, the URANS turbulence models must be used as hybrid methods such as DES and LES methods require a three-dimensional simulation such as an infinite wing. As this can become costly, in particular for investigations such as stall flutter, evaluations of the other numerical parameters are typically undertaken in two dimensions, while the final simulation is completed with a periodic (semi-infinite) wing. ...
Conference Paper
A solver has been developed within the OpenFoam framework to compute large amplitude motion of two-dimensional rigid configurations. The results obtained with this code were successfully validated on rigid airfoils at static and dynamic conditions, as well as correlated with experimental data and numerical solutions from similar unsteady solvers. The results demonstrated that while current computational methods are able to predict the self-sustained oscillations characterizing a pitch-dominated stall flutter, including energy transfer, improvements are needed. The influence of grid, temporal integration, turbulence modeling, and flow equations is examined for the stall flflutterstarting solution of dynamic stall.
... The 2D OA209 stall case [7] allows some requirements to be defined in terms of turbulence modeling and grid resolutions [9] [10]. An extensive analysis of the time resolution has been proposed by Liggett et al. for the case of VR7 airfoil in dynamic stall condition [12]. More recently, the configuration of an oscillating finite-span 3D wing has been investigated numerically [13][14] [15] and validated with the experimental data of Ref. [8]. ...
... Liggett et al. performed a deep investigation of the influence of the time resolution for the prediction of 2D airfoil dynamic stall [12]. In the framework of an implicit second order time scheme, they have shown that the value of the (number of time steps per cycle) x (number of sub-iterations of the Newton iterative process) should be high enough to capture stall onset and flow reattachment. ...
Conference Paper
Full-text available
Helicopter rotor blades in high thrust forward flight or in stiff maneuvers undergo dynamic stall. This phenomenon is due to complex unsteady three-dimensional flow separation mechanisms on the retreating blade that can lead to structural damage of the pitch links. The understanding and the accurate numerical prediction of dynamic stall are still challenging problems. In the continuity of previous studies focused on simplified configurations of 2D airfoil and 3D finite span wing, the dynamic stall on an isolated rotor in high thrust forward flight is investigated. A particular attention has been paid to the time and space resolution necessary to capture the stall phenomenon. The comparison with experiment in terms of section loads and pitching moments is in satisfactory agreement. The time evolution of the flow separation provided by the simulation is deeply analyzed and a scenario involving different stall mechanisms is proposed in order to explain the occurrence of the strong variations of loads and pitching moments on the retreating blade.
... Dans leur étude très complète, Liggett et Smith [66] soulignent la nécessité de converger leur méthode itérative afin d'atteindre une précision au second-ordre. Ils montrent également que, pour les modélisations utilisées (modèle k-ω SST, HRLES), la convergence en temps n'est que qualitative en écoulement décollé, contrairement à un écoulement attaché. ...
... Ainsi, la discrétisation temporelle a une forte influence sur la prévision des charges aérodynamiques et du décrochage dynamique. Cela a déjà été évoqué par différentes équipes de recherche sur des configurations simplifiées [66,110] ou plus réalistes [96,120]. ...
Thesis
Le décrochage dynamique se produit sur les rotors d’hélicoptère fortement chargés ou à grande vitesse d’avancement. Il engendre des efforts dynamiques importants et d’intenses vibrations, limitant le domaine de vol des hélicoptères. L’objectif de ces travaux de thèse est de mettre à profit les outils de simulation aéroélastique afin d’identifier les mécanismes déclencheurs du décrochage dynamique en conditions réalistes d’un vol d’avancement à forte charge. Le dépouillement de bases de données d’essais rotor de l’ONERA, conforté par des simulations “basse fidélité”, a permis de sélectionner un ensemble de points d’essais pertinents et représentatifs du décrochage dynamique, pour différentes conditions de vol et géométries de pale. L’analyse détaillée des configurations sélectionnées s’appuie sur des calculs de couplage faible entre le code fluide elsA et le code structure HOST. Des outils de post-traitement ont été développés et utilisés pour localiser et caractériser les décollements de la couche limite, ainsi que pour en identifier les mécanismes déclencheurs. L’analyse de ces post-traitements révèle différentes régions de décollement sur le disque rotor. Nous observons notamment un décollement subsonique dans le troisième quadrant fortement influencé par une interaction pale-tourbillon. D’autre part, des décollements en pied de choc apparaissent sur la pale arrière et sur le premier quadrant pour lesquels la réponse en torsion est impliquée. Une étude a été menée afin d’isoler chacun de ces mécanismes, et plus particulièrement l’interaction pale-tourbillon. Pour cela, nous avons réalisé des simulations simplifiées modélisant une pale isolée non-tournante soumise ou non à une telle interaction. Les résultats semblent confirmer que cette interaction pale-tourbillon joue un rôle majeur dans le déclenchement du décrochage dynamique pour de nombreuses configurations de vol d’avancement.
... More information on blending functions is available in Lynch & Smith (2011) and Smith et al. (2013). It has been demonstrated that an approach which resolves turbulence in the wake, such as HRLES, is necessary for massively separated flows around airfoils undergoing static and dynamic stall (Sánchez-Rocha, Kirtas & Menon 2006;Liggett & Smith 2012) and bluff bodies (Theron et al. 2006;Lynch & Smith 2011;Shenoy et al. 2013;Prosser & Smith 2014). ...
... Here, u * is the friction velocity, u * = √ τ w /ρ, and τ w is the shear stress at the wall. It has been previously demonstrated that a y + value and number of normal-growth-layer cells similar to those applied here are important to capture separation and reattachment on surfaces at high angles of incidence (Lynch & Smith 2011;Smith et al. 2011;Liggett & Smith 2012). Figure 3 shows representative views of the grid spacing on the surface. ...
Article
Three-dimensional bluff body aerodynamics are pertinent across a broad range of engineering disciplines. In three-dimensional bluff body flows, shear layer behaviour has a primary influence on the surface pressure distributions and, therefore, the integrated forces and moments. There currently exists a significant gap in understanding of the flow around canonical three-dimensional bluff bodies such as rectangular prisms and short circular cylinders. High-fidelity numerical experiments using a hybrid turbulence closure that resolves large eddies in separated wakes close this gap and provide new insights into the unsteady behaviour of these bodies. A time-averaging technique that captures the mean shear layer behaviours in these unsteady turbulent flows is developed, and empirical characterizations are developed for important quantities, including the shear layer reattachment distance, the separation bubble pressure, the maximum reattachment pressure, and the stagnation point location. Many of these quantities are found to exhibit a universal behaviour that varies only with the incidence angle and face shape (flat or curved) when an appropriate normalization is applied.
... Zanotti et al. [70] also emphasized the necessity of three-dimensional modeling for simulations of deep dynamic stall. Liggett and Smith [71] [73]) in case of massively separated flow and achieved good agreement with PIV data for a pitching NACA 0012 airfoil in reverse-flow dynamic stall. Also, Visbal and Garmann [74] and Benton and Visbal [75] carried out very high-fidelity, wall-resolved LES of the onset of dynamic stall on a pitching NACA 0012 airfoil at Reynolds numbers up to one million. ...
... These findings are consistent with a time step dependency study carried out before [38] based on the RTG case that showed that a further reduction of the time step had no significant influence on integral lift and pitching moment. However, other numerical investigations of separated flow around airfoils or finite wings [134,71,94,80] used much smaller time steps -especially if a DES was carried out -on the order of ∆t = ∆ 0 /u max , with ∆ 0 being the smallest grid size and u max the largest flow velocity in the respective region. ...
Thesis
Full-text available
High-fidelity CFD simulations of helicopter rotors are carried out to investigate the dynamic stall flow phenomenon. The simulations are based on two experimental test cases, namely a model rotor with high cyclic pitch control operated at DLR Göttingen, and a highly-loaded, high-speed turn flight of the Bluecopter demonstrator. URANS and DDES simulations are carried out using the flow solver FLOWer coupled with CAMRAD II. A validation of the numerical methods is conducted based on the experimental model-rotor case, which shows that the onset of dynamic stall and the associated load overshoots agree well in overall. An unprecedented comparison of instantaneous PIV and CFD results reveals that after stall onset, only the DDES captures the chaotic nature of separated flow and exhibits small-scale vortical structures that correlate nicely with the measurement. However, the DDES suffers from the numerical artifact of modeled-stress depletion leading to grid-induced separation. Therefore, several improvements to the so-called boundary-layer shielding are investigated for both dynamic stall cases and found to eliminate the issue. Also, a shear-layer-adaptive filter width is successfully applied to the LES mode of the DDES that promotes a more realistic development of flow instabilities in separated shear layers. Concerning the turn flight simulation of the Bluecopter, the computed main rotor control angles agree very well with the flight-test measurements. A comparison of the pitch-link loads shows a good correlation regarding the overall trends and a significant improvement over a lower-order analysis. However, the pitch-link-load amplitudes are still underpredicted. Furthermore, the flow field is found to be highly unsteady and complex throughout a large portion of the azimuth, exhibiting strong separation and multiple dynamic stall events that are partly triggered by blade-vortex interaction.
... The boundary layer region of the grids used prismatic elements aligned with the wall-normal direction; at least 35 cells in the normal direction with a nondimensional wall spacing (y + ) of less than 1.0. This boundary layer spacing is necessary to correctly capture separation and reattachment on surfaces at high angles normal to the flow [20,24,29] . ...
Conference Paper
Full-text available
Fundamental three-dimensional aerodynamic phenomena have been investigated for small-aspect-ratio rectangular prisms and circular cylinders, canonical bluff body geometries representative of typical helicopter sling loads. A detailed identification and quantification of the unsteady aerodynamic phenomena at differing orientation angles associated with instabilities has been undertaken. The numerical experiments indicate that shear layer reattachment is the primary factor in determining the mean forces and moments of the bluff bodies. Many characteristics of the shear layer behavior are similar for the three-dimensional bluff bodies and, in some cases, similar to two-dimensional behavior extant in the literature. Differences in the canonical shape and aspect ratios occur and are quantified with varying reattachment distances as the orientation changes. Strouhal numbers vary in the range from 0.15-0.3 and exhibited a highly three- dimensional, multimodal nature at the Reynolds numbers investigated. These findings are significant for the development of reduced-order aerodynamic modeling of sling loads. Copyright © (2014) by the Royal Aeronautical Society. All rights reserved.
... This value is relatively small, but has been shown to be sufficient in forward flight (Ref. 26) given the minor fluctuations from cycle to cycle. The phaseaveraged unsteady airloads are provided in Fig. 10. ...
Conference Paper
Two fundamental models of the flow (static and dynamic) over airfoils in the reverse How region of a helicopter in forward flight are investigated experimentally and computationally at Reynolds numbers of O(105). The first model examines the time-averaged and unsteady flow resulting from a two-dimensional NACA 0012 airfoil held at a static angle of attack. Computational tools successfully predict the presence of three unsteady wake regimes and time-averaged airloads measured experimentally at the University of Maryland (UMD). A second model is investigated by pitching a NACA 0012 airfoil through deep dynamic stall in reverse flow. Both experimental and computational results reveal flow separation at the sharp leading edge for shallow angles of attack, leading to the early formation of a reverse flow dynamic stall vortex. Subsequent flow features in the pitching cycle (trailing edge vortex, secondary dynamic stall vortex) are also captured by the numerical simulation, although the timing and strength of some of these features do not align completely with experiment. This work gives fundamental insight of the aerodynamic behavior of airfoils in reverse flow towards a better understanding of the complex nature of the reverse flow region as well as promising new computational tools to be used in the simulation of this unique flow regime.
... As shown in Fig. 13, the change in lift and pitching moment between 3000 and 18,000 time steps per period is lower than the cycle-to-cycle variation and, therefore, the two cases have the same temporal convergence level. The use of 18,000 time steps has been shown in Ref. 23 to be sufficient for other dynamic stall simulations with similar turbulence closures to guarantee second-order temporal accuracy, as was observed in these simulations. ...
Article
Three-dimensional numerical computations using ONERA's structured elsA code and the unstructured DLR-TAU code are compared with the OA209 finite wing experiments in static stall and dynamic stall conditions at a Mach number of 0.16 and a Reynolds number of 1 × 106. The DLR-TAU computations were run with the Spalart—Allmaras and Menter shear stress transport (SST) turbulence models, and the elsA computations were carried out using the Spalart—Allmaras and the k—ω Kok + SST turbulence models. Although comparable grids were used, the static simulations show large discrepancies in the stall region between the structured and unstructured approaches. Large differences for the three-dimensional dynamic stall case are obtained with the computations using the Spalart—Allmaras turbulence model showing trailing edge separation only in contrast to the leading edge stall in the experiment. The three-dimensional dynamic stall computations with the two-equation turbulence models are in good agreement with the unsteady pressure measurements and flow field visualizations of the experiment, but also show a shift in the stall angle compared to the experiment. The analysis of the flow field around the finite wing using the numerical simulations reveals the evolution of the Ω-shaped vortex, generated by the interaction of the blade tip vortex.
... In this work, HRLES data validated for turbulent bluff body flows including dynamic cases (Refs. 17,[21][22][23][24][25][26] have been employed to generate the quasi-steady data set. The details of the solver, grids, and conditions for the computation of quasi-steady aerodynamic coefficients for 3D rectangular prism and cylinder geometries have been presented previously (Refs. ...
Article
A novel reduced-order model for the simulation of bluff bodies in unsteady, arbitrary motion has been developed. The model is physics-based, meaning that it is derived from known fundamental aerodynamic phenomena of bluff bodies instead of response fitting of experimental data. This physics-based approach is essential to ensure that the model is applicable to new, untested configurations. We describe the development of a physics-based model, including detailed explanations of the fundamental aerodynamic phenomena and how they are modeled in simulation. The reduced-order model is evaluated by application to rotorcraft-tethered loads and validated against much more expensive high-fidelity computational fluid dynamics simulations and flight tests. Excellent correlation in the predictions of aerodynamic forces and moments, as well as the dynamic response, is observed, while the computational cost has been reduced by several orders of magnitude relative to high-fidelity computational-fluid-dynamics-based simulations. Additionally, the important role that unsteady aerodynamics play in bluff body dynamics and instability is demonstrated.
... Each cylindrical section was meshed using a structured O-grid, spanned by (256 × 128 × 295) points in the azimuthal, spanwise and radial directions, respectively. The grid spacing at the wall corresponds to y + < 1 for the highest Reynolds number, with at least 50 points resolving the boundary layer [45] . The simulations were accomplished with a physical time-step ∆t × u ∞ × D = 0.01, yielding approximately 200 iterations per vortex shedding cycle. ...
Conference Paper
Full-text available
A new turbulence approach is proposed that combines the strengths of Unsteady Reynolds-Averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) turbulence closure with local dynamic kinetic model (LDKM) and the widely adopted γ − Re θ t transition model. This method has the potential for accurately capturing massively separated boundary layers in the transitional Reynolds number range at a reasonable computational cost, and therefore holds great promise for the rotorcraft industry. Comparisons are evaluated on several cases, including a transitional flat plate, circular cylinder in crossflow and NACA 63-415 wing. Cost and accuracy correlations with URANS and prior hybrid URANS-LES approaches with and without transition modeling indicate that this new method can capture both separation and transition more accurately and cost effectively.
... Among the various approaches developed in the last decades (Large Eddy Simulation, Organized Eddy Simulation, Detached Eddy Simulation, Zonal Detached Eddy Simulation, hybrid RANS/LES...), the classical Reynolds-Averaged Navier Stokes (RANS) approach is primarily applied in the design of airfoils. But the leading edge stall is not accurately predicted for two primary reasons, (i) the inability of turbulence models to capture separated turbulent flows and laminar-turbulent transition of the boundary layer [7,27] , and (ii) numerical issues for determining time-independent solutions of the RANS equations around the stall angle of attack [17] . The determination of fixed points of the RANS equations is a prerequisite in recent stability analysis, which aims to understand the onset of large-scale low-frequency fluctuations in high-Reynolds number flows [22,31] . ...
Article
The Selective Frequency Damping (SFD) method introduced by Akervik et al. [1] to obtain steady laminar solutions of the Navier-Stokes equations is used to compute steady turbulent solutions of the RANS equations. Coupling the SFD to a classical time step algorithm improves the convergence and robustness of the steady state algorithm. This is demonstrated on the turbulent flow solutions around an airfoil at high Reynolds number (Re ~ 106) and for angles of attack near stall. The existence of multiple steady solutions, a key element for explaining the hysteresis phenomenon, is reported and described.
... The importance of the laminar-turbulent transition modeling for 2-D dynamic stall computations was noticed in [7,8]. Richter et al. [8] and Liggett and Smith [9] studied the spatial and temporal aspects of 2-D dynamic stall cases and showed that two-dimensional computations tend to overestimate the aerodynamic peak values of the experimental data during deep dynamic stall. Klein et al. [10] demonstrated that dynamic stall computations inside a wind tunnel are very sensitive to the prediction of corner separation, and the use of different turbulence models results in large discrepancies with each other and with the experimental data. ...
Article
Full-text available
Unsteady Reynolds-averaged Navier-Stokes computations were carried out on a pitching finite wing model using the finite volume solver DLR-TAU. The comparison with the experimental data reveals a good agreement, especially in the region of the first occurrence of stall. Discrepancies are observed in the blade tip region, where the flow in the numerical data shows a stronger separation along with larger hysteresis effects in contrast to the experiment. An investigation with different pitching frequencies revealed a change in the sequence of dynamic stall vortex formation in the spanwise direction. For the lowest frequency the propagation of the stall vortex starts at the wing tip and then spreads rootwards, whereas for the higher frequencies the first evolution of the dynamic stall vortex starts further inboard, subsequently propagating in tipward and rootward directions. An investigation using a γ-Reθt approach demonstrated that small differences can be attributed to transition, nevertheless these can give further insight in the physics of dynamic stall and improve the comparability with the experiment. A comparison with two-dimensional simulations shows strong similarities in the sections where the vortex starts to evolve and large differences in the surrounding areas.
... The importance of the laminar-turbulent transition modeling for 2-D dynamic stall computations was noticed in [7,8]. Richter et al. [8] and Liggett and Smith [9] studied the spatial and temporal aspects of 2-D dynamic stall cases and showed that two-dimensional computations tend to overestimate the aerodynamic peak values of the experimental data during deep dynamic stall. Klein et al. [10] demonstrated that dynamic stall computations inside a wind tunnel are very sensitive to the prediction of corner separation, and the use of different turbulence models results in large discrepancies with each other and with the experimental data. ...
Article
Unsteady Reynolds-averaged Navier–Stokes computations were carried out on a pitching finite wing model using the finite volume solver DLR-TAU. The comparison with the experimental data reveals a good agreement, especially in the region of the first occurrence of stall. Discrepancies are observed in the blade tip region, where the flow in the numerical data shows a stronger separation along with larger hysteresis effects in contrast to the experiment. Additionally, the analysis of the flowfield reveals the existence of multiple dynamic stall cells over the span. The simulations with different pitching frequencies demonstrate a change in the topology of dynamic stall vortex formation in the spanwise direction. An investigation using turbulence transition modeling based on a γ − Reθt approach demonstrated that small differences can be attributed to transition; nevertheless, these can give further insight into the physics of dynamic stall and improve the comparability with the experiment. A comparison with two- dimensional simulations shows strong similarities of the peak values in the sections where the vortex starts to evolve and, although the three-dimensional flow is strongly driven by spanwise flow, the impact on the aerodynamic loads is relatively low. DOI: 10.2514/1.C034020
... Simulations used 9000 time steps per cycle with 30 Newton subiterations per time step and second order time-advancement. Based on Ref. [28], this is sufficient to capture flow field features needed for this study. The numerical scheme used Euler central differencing with the ARC3D diagonalized Beam-Warming scalar pentadiagonal scheme and the TLNS3D dissipation scheme. ...
... The results presented in this paper focus on the same or similar configurations that have been extensively studied by the second author's group. Mesh sensitivities for the earlier HRLES model have been presented in numerous previous works [43,44,[53][54][55][56]. All of the current simulations here and in Hodara [55] support that the conclusions from previous mesh and time step sensitivity studies (on both transition and hybrid filter methods) can be applied to the new approach. ...
Article
The numerical prediction of transition from laminar to turbulent flow has proven to be an arduous challenge for computational fluid dynamics, with few approaches providing routine accurate results within the cost confines of engineering applications. The recently proposed y-Reθ transition model shows promise for predicting attached and mildly separated boundary layers in the transitional regime, but its accuracy diminishes for massively separated flows. In this effort, a new turbulence closure is proposed that combines the strengths of the local dynamic kinetic energy model and the widely adopted y-Reθ transition model using an additive hybrid filtering approach. This method has the potential for accurately capturing massively separated boundary layers in the transitional Reynolds number range at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, NACA 63-415 wing, and circular cylinder in crossflow. The new closure captures the physics associated with a separated wake (circular cylinder) across a range of Reynolds numbers from 10 to 2 million (2 × 10⁶) and performed significantly better in capturing performance and flowfield features of engineering interest than existing turbulence models. The transitional hybrid approach is numerically robust and requires less than 2% extra computational work per iteration as compared with the baseline Langtry.Menter transition model.
... Die Schwankungen während des Aufnickens sind dabei ein Resultat der stumpfen Blattwurzel, an der es während der gesamten Nickschwingung zu Wirbelablösungen kommt. Die aerodynamischen Beiwerte der 4. und 5. Periode weisen nur noch geringe Unterschiede auf, weshalb die 5. Periode der Simulation als ausreichend konvergiert betrachtet wird.Liggett et al.[55] zeigten, dass eine Anzahl von 18000 Zeitschritten pro Periode für Dynamic Stall-Simulationen mit einem ähnlichen Turbulenzmodell ausreicht, um eine zeitliche Diskretisierung zweiter Ordnung zu gewährleisten. Um den Einfluss des physikalischen Zeitschrittes der DLR-TAU-Simulationen zu überprüfen, wird daher die fünfte Nickschwingung unter Verwendung von 18000 Zeitschritten pro Periode wiederholt. ...
Article
Der dynamische Strömungsabriss (engl.: Dynamic Stall) schränkt die Fluggeschwindigkeit und Agilität von Hubschraubern ein und wird seit Jahrzehnten intensiv erforscht. In dieser Arbeit werden umfangreiche URANS-Simulationen mit dem unstrukturierten Finite-Volumen-Löser DLR-TAU durchgeführt, um die dreidimensionalen Effekte des dynamischen Strömungsabrisses zu analysieren. Die Untersuchungen finden am ONERA-Blattspitzenmodell bei einer Machzahl von 0.16 und einer Reynoldszahl von 10e6 sowie am DLR-­Blattspitzenmodell bei einer Machzahl von 0.16 und einer Reynoldszahl von 9 x 10e5 statt. Die Simulationen an der ONERA-Blattspitze werden mit Windkanaldaten validiert und anhand von Simulationen mit dem struktierten elsA-Code verglichen. Während es in den URANS-Simulationen unter Verwendung des Spalart-Allmaras-Turbulenzmodells lediglich zu einer Hinterkantenablösung ohne Übereinstimmung mit den experimentellen Daten kommt, wird mit dem SST-Turbulenzmodell eine qualitative Übereinstimmung mit dem Experiment erzielt. Die Simulationen zeigen die Bildung einer Q-förmigen Wirbelstruktur, die die Aerodynamik am Modell prägt und mit spannweitigen Geschwindigkeiten V > 1 x U einhergeht. Am DLR-Blattspitzenmodell bilden sich aufgrund der großen Spannweite sogar mehrere Q-förmige Wirbel, wobei die Schwingungsfrequenz die Topologie des Ablöseprozesses beeinflusst. Bei der niedrigsten untersuchten Frequenz breitet sich die Ablösung von der Blattspitze heraus, während höhere Frequenzen dazu führen, dass sich der Wirbel bei 60% Spannweite zu bilden beginnt. Für die Dynamic Stall-Vorhersage ist auch die Transitionsmodellierung wichtig, jedoch ändern sich in dieser Studie die integralen Beiwerte im Vergleich zu vollturbulenten Simulationen nur geringfügig. Die zweidimensionalen Simulationen zeigen, dass die Beiwerte an der Ablöseposition vergleichbar mit denen der dreidimensionalen Simulationen sind, während größere Unterschiede in weiter entfernten Positionen vorhanden sind. Beim Blattspitzenwirbel kommt es während des betrachteten Dynamic Stall-Falls zu starken Hystereseeffekten zwischen dem Auf-und Abnicken des Flügels. Die Untersuchungen liefern einen wichtigen Beitrag zum besseren Verständnis des dynamischen Strömungsabrisses, einer Grundvoraussetzung für die Weiterentwicklung moderner Hubschrauber.
... For most rotorcraft applications where the flow is at higher Reynolds Numbers, simulations to better understand dynamic stall have been carried out with Reynolds Averaged Navier Stokes (RANS) and Detached Eddy Simulation (DES) based methods with different turbulence closure models (Refs. [2][3][4][5][6]. In past design studies (Refs. ...
Conference Paper
Full-text available
Rotor blade aerodynamics are significantly influenced by dynamic stall. The objective of this study is to use a combined experimental/computational approach toward better understanding of the dynamic stall phenomenon on the SC1094R8 airfoil. This study is part of a larger effort to alleviate the adverse effects of dynamic stall on rotor blade aerodynamics through airfoil shape optimization. In order to accomplish this goal, time-accurate surface pressure measurements along with lift and moment coefficients are gathered experimentally. Boundary layer tripping is performed to ensure behavior similar to that of the airfoil at larger Reynolds numbers. Sensitivity of dynamic stall under different flow conditions is also studied. Numerical simulations have been performed for similar flow conditions and compared with the experimental results. The result have aided in clarifying the sensitivity of dynamic stall as well as providing encouraging indications of the ability of the simulations to capture the important features associated with dynamic stall. © 2017 by the American Helicopter Society International, Inc.
... Martinat et al. [37] investigated the turbulent effect of NACA 0012 airfoil under dynamic stall, and demonstrated the strong three-dimensional turbulence effects along the span in the downward stroke of pitching motion. Liggett and Smith [38] explored the temporal convergence and accuracy of simulating an airfoil under both static and dynamic stall conditions, and obtained a true second order accurate solution. Lu et al [39] investigated the effect of asymmetric sinusoidal motion on pitching airfoil aerodynamic for flowing around a NACA0012 airfoil, and acquired the airfoil leading edge vortex characteristic. ...
Article
This paper performs the detailed simulation analyses of airfoil-based piezoaeroelastic energy harvester with two degrees of freedom self-induced plunge-pitch motions, for exploring the flow field characteristic and enhancing the harvesting performance. The designing of the harvester for achieving flutter is first accomplished, finite element model is then built and simulation analyses are performed, and a prototype of the harvester system is finally fabricated. The obtained simulation results are in good agreement with the experimental and theoretical values. The effects of the key structural parameters of the harvester on flow field, aeroelastic vibration, and harvesting performance are numerically investigated. The results demonstrated that the structural parameters of the harvester determine primarily flutter onset of velocity, and consequently affect the dynamic behavior and harvesting performance. The harvester system takes place flutter and occurs limit cycle oscillations after flutter onset of velocity, which is suitable for harvesting energy. The smaller pitch structural stiffness coefficient and the more moderate both plunge stiffness and pitch damping coefficients are, the better aeroelastic vibration and output performance can be captured. A maximum output voltage of 29.08 V and output power of 3.382 mW can be harvested when the linear and cubic structural stiffness coefficients in pitch are 2.5 N·m and 100 N·m at 14 m/s, respectively, which corresponds to the power density of 21.138 mW/cm³ and demonstrates the superior harvesting performance over others. This work provides a significant guidance for designing the more efficient airfoil-based piezoaeroelastic energy harvester utilized in unmanned aerial vehicles.
... For cases involving laminar-turbulent transition, it was found that better accuracy was obtained using a combination of smaller time steps with reduced sub-iterations. Smith et al. [199] further investigated the issue and showed that it is critical to have a time step small enough to achieve true second-order temporal convergence. With that in mind, three resolutions STAR-CCM+. ...
Thesis
Full-text available
Traditional rotorcraft airfoil design is based on steady-flow aerodynamic requirements. The approach assumes a strong correlation between steady and unsteady aerodynamic characteristics, which is often not observed in practice. This is particularly relevant at high speed and high thrust conditions, when the rotor is susceptible to dynamic stall and its many negative consequences. Given the abrupt nature of the phenomena, large margins are typically established to prevent fatigue loads on the blades and pitch links; thus, limiting operation under high altitudes, high payloads, high temperatures, as well as during maneuvers. This work addresses the problem from the perspective of passive airfoil design. Typical design requirements are revisited to include metrics for improved dynamic stall and new ways to qualifying rotorcraft airfoils are proposed. A number of design studies are conducted to better understand the relation between airfoil shape and dynamic stall behavior. The design manipulations are handled by an inversedesign, conformal mapping method, and unsteady Reynolds-averaged Navier-Stokes equations are used to predict the aerodynamic performance under pitch motion. In unsteady flow, the occurrence of aerodynamic lags in the development of pressures, boundary-layer separation, and viscous-inviscid interactions suggest more strict requirements than in steady flow. In order to postpone the onset of dynamic stall, the design needs to handle competing leading- and trailing-edge separation mechanisms, which are heavily influenced by local supersonic flow, strong shock waves, and laminar-turbulent transition effects. It is found that a particular tailoring of the trailing-edge separation development can provide adequate dynamic stall characteristics and minimize penalties in drag and nose-down pitching moment. At the same time, a proper design of the nose shape is required to avoid strong shock waves and prevent premature leading-edge stall. A proof-of-concept airfoil is developed to improve dynamic stall behavior, while meeting stringent requirements on flight conditions away from stall. Trade-offs to the achievement of typical rotor design requirements are discussed. Performance calculations using information obtained from comprehensive analysis (RCAS) based on a UH-60A helicopter are conducted to estimate gains in the rotor stall boundaries. Results are compared to the baseline UH-60A rotor, as well as a blade that uses a VR-12 airfoil inboard. It is found that the new airfoil can provide expansion of the operational envelope compared to the other two configurations, while still reducing hover drag and maintaining very low pitching moments. Some compromises in the drag rise at high Mach numbers are found in comparison to the VR-12 airfoil. By placing the new airfoil up to r/R = 0.80 on the rotor, the baseline UH-60A maximum speed (μ = 0.37) can be achieved with considerable margins to drag rise. Finally, pitching wing calculations are conducted to demonstrate the proposed concepts in three-dimensional flow. Differences in the development of stall between wings using a VR-12 airfoil and the new airfoil are discussed. Despite the complex evolution of 3-D flow structures, the stall onset mechanisms seem to follow the trends obtained with 2-D simulations. The new wing experiences a more favorable dynamic stall inception and considerable decreases in the integrated (3-D) peak pitching moments. The results are promising and give confidence in the design approach. The applied methodology can aid with the design of airfoils that are more suited for operation at high loading conditions.
... Liggett and Smith (Ref. 7) used unsteady Reynolds-averaged Navier-Stokes (URANS) and hybrid Reynolds-averaged Navier-Stokes/large-eddy simulations (RANS/LES) to investigate dynamic stall on a pitching VR7 airfoil and demonstrated the importance of temporal convergence to reduce phase-shift errors in load predictions. Thanks to the ever increasing computational power, Visbal and Garmann (Ref. ...
Conference Paper
Full-text available
A highly loaded, high-speed turn flight of Airbus Helicopters' Bluecopter demonstrator helicopter is simulated using a loose computational fluid dynamics/structural dynamics (CFD/CSD) coupling of the flow solver FLOWer and the rotorcraft comprehensive code CAMRAD II. The rotor aerodynamics is computed using a high-fidelity delayed detached-eddy simulation (DDES). A three-degree-of-freedom trim of an isolated rotor is performed, yielding main-rotor control angles that agree well with the flight-test measurements. The flow field in this flight condition is found to be highly unsteady and complex, featuring massively separated flow, blade-vortex-interaction, multiple dynamic-stall events and shock-induced separation. The trim target rotor thrust, turbulence model and considered helicopter components like the fuselage are varied. Then, the computed pitch-link loads are compared to flight-test measurements. It shows that all CFD/CSD cases underpredict the amplitudes of the flight test and yield phase shifts. However, overall trends agree reasonably. Also, the SST DDES turbulence model performs better than Spalart-Allmaras (SA) DDES and the consideration of the rotor hub and fuselage improves the agreement with flight-test data.
Chapter
Full-text available
Dynamic stall phenomenon on a Boeing Vetrol-VR-7 airfoil, oscillating at quarter chord with reduced frequency of 0.1, is investigated at three different slot configurations—leading edge, trailing edge and combination of this two edges at a Reynolds number of 2.5 × 106. It is shown that the use of a leading-edge slot can eliminate the dynamic stall vortex (DSV) and increase the lift coefficient by 20%, and a decrease in the drag and moment coefficient by more than 70%. It is computed that the performance at low angles of attack can be improved with the use of a non-drooped leading edge in the airfoil. Furthermore, the combination of a leading and trailing-edge slots further improves the lift characteristics.
Article
Active trailing-edge flaps are a method of aerodynamic control under extensive research to reduce the detrimental effects of dynamic stall. Physical phenomena are poorly understood in the context of active flaps including vorticity and acoustics, separation, and transition. In addition, discrete trailing-edge flaps create a cavity-like flow within the airfoil-flap gap that can complicate these phenomena. This work has explored the physical response of a static airfoil with a discrete noncontoured oscillating flap over a range of freestream parameters. The effects of attached and separated flows, flap oscillation scheduling, airfoil-flap gap size, and freestream speed have all been investigated. Time-accurate predictions were performed using a hybrid Reynolds-averaged Navier-Stokes/large eddy simulation turbulence model. Trailing-edge stall suppression and an increase between aerodynamic response and deflection input were observed as the flap oscillation frequency increased. The lag between response and input also increased approximately linearly with airfoil-flap gap size. Results indicated the transition was unaffected by the flap oscillations. During the frequency content of flow the unsteadiness was consistent with separated flow driven by the flap. Discrete noncontoured flaps are not recommended; if they are required, the size of the gap should be minimized to maintain performance and reduce lag.
Conference Paper
Turbulence and transition modeling still accounts for most of the uncertainties in numerical modeling of complex flows associated with rotorcraft vehicles and components. Computational fluid dynamics (CFD) methods typically cannot capture complex physics with traditional Reynolds-averaged Navier-Stokes (RANS)-based models since majority of physics are transient and occur at different scales. Over the past decade, a resurgence in research related to turbulence modeling has resulted in new large eddy simulation (LES)-based turbulence techniques that have improved computations that involve separated flows. The accuracy of a hybrid RANS-LES technique, first shown to improve turbulent predictions on rotors in the DARPA Quiet Helicopter program, have been increased via locally varying coefficients.
Chapter
Full-text available
Rising greenhouse gas emission and global warming compel the world community to look for renewable energy sources to generate power. The renewable wind energy provides an alternative to fossil fuel. A significant research attention has been placed on the use of vertical axis wind turbine due to its low-wind operational capability. However, the effectiveness of traditional vertical axis wind turbines (VAWT) in built-up areas is below expectation. Therefore, the primary objective of this study is to develop a single stage drag-based multi-blade micro vertical axis wind turbine which can generate a reasonable amount of torque and power in complex wind conditions in built-up areas.
Conference Paper
A low-Reynolds number rectilinear analog of the retreating-blade problem is considered by computationally and experimentally studying a NACA0012 blade in spanwise oscilla-tion in a free stream. Three-dimensional hybrid RANS-LES simulations with spanwise periodic boundary conditions and experimental flow visualization support the description of experimental direct force measurements for a wide range reduced frequencies and advance ratios, including fully reversed flow conditions. A fixed incidence of 6 degrees is taken as a nominally attached-flow case, and agrees reasonably well with Isaacs' theory. A fixed incidence of 20 degrees is taken as a fully-separated case, and departs markedly from invis-cid theory, and even more so from quasi-steady approximation. Experimental-computational comparison shows a computational overprediction of lift relative to experimental results, at moderate advance ratios. Agreement in fully reversed flow is, however, quite good.
Article
The numerical simulation of dynamic stall around a 3D finite-span oscillating wing of constant OA209 airfoil section is compared to experimental results obtained in the ONERA F2 wind-tunnel, assuming fully turbulent flow. A deep dynamic stall case is considered for a reduced frequency typical of helicopter problems. A detailed comparison with the experimental data available (unsteady pressure distribution and velocity field) shows that the main flow features are captured by the numerical simulation, more especially the large spanwise flow component induced by separation.
Article
A highly loaded, high-speed turn flight of Airbus Helicopters’ Bluecopter demonstrator helicopter is simulated to investigate dynamic stall using a loose computational fluid dynamics/structural dynamics (CFD/CSD) coupling of the flow solver FLOWer and the rotorcraft comprehensive code CAMRAD II. The rotor aerodynamics is computed using a high-fidelity delayed detached-eddy simulation (DDES). A three-degree-of-freedom trim of an isolated rotor is performed, yielding main-rotor control angles that agree well with the flight-test measurements. The flow field in this flight condition is found to be highly unsteady and complex, featuring massively separated flow, blade–vortex interaction, multiple dynamic-stall events, and shock-induced separation. The computed pitch-link loads are compared to flight-test measurements. This shows that all CFD/CSD cases underpredict the amplitudes of the flight test and yield phase shifts. However, overall trends agree reasonably. Also, varying the computational setup reveals that the shear stress transport–DDES turbulence model performs better than Spalart–Allmaras–DDES, that the consideration of the rotor hub and fuselage improves the agreement with flight-test data, and that the elastic twist plays only a minor role in the dynamic-stall events.
Article
High-resolution computational fluid dynamics (CFD) predictions of static and dynamic stall of a finite-span ONERA OA209 wing were validated against the wind tunnel test measurements. The freestream Mach number was 0.16 and the Reynold number was 1 million. For the dynamic stall study, a sinusoidal pitching motion was prescribed. The CFD modeling approaches employed were — Delayed Detached Eddy Simulation (DDES) modeling using the NASA OVERFLOW flow solver, Unsteady Reynolds-averaged Navier–Stokes (URANS) modeling using the ONERA elsA flow solver, and DDES modeling using the NASA FUN3D flow solver. The flow was modeled as both fully turbulent and transitional. A comparative study between predictions and the wind-tunnel test data for pre- and post-stall measurements was carried out that included wing section lift and moment, surface pressure, and velocity field at chordwise and spanwise planes. The high spatial and temporal resolutions employed resulted in good correlations with the test data, in particular with the inclusion of DDES modeling along with a turbulence transition model. The CFD modeling parameters thus establish were applied to a deep and a light stall cases, and were found to accurately capture the wing section loads, demonstrating its generalizability in capturing the stall dynamics.
Article
Numerical computations of three-dimensional dynamic stall on a two-bladed model rotor (R=0.65m, M75=0.21, Re75=3.5×10[5]) with 1/rev cyclic pitch control are presented and compared to experimental surface pressure and particle image velocimetry data. In addition to unsteady Reynolds-averaged Navier–Stokes (URANS) simulations using the finite-volume flow solvers FLOWer and TAU, a delayed detached-eddy simulation (DDES) with Menter shear-stress transport (SST) as underlying Reynolds-averaged Navier–Stokes (RANS) model is carried out with FLOWer. Facing dynamic stall and flow separation, the DDES reproduces high-frequency load fluctuations, cycle-to-cycle variations, and small-scale vortical structures observed in the experiment, unlike the URANS results. However, common hybrid RANS/large-eddy simulation issues—grid-induced separation (GIS) and the gray area problem—play a role in this DDES and influence loads severely. FLOWer SST simulations yield load peaks of the same magnitude as individual, non-phase-averaged measurements. With TAU SST, the dynamic stall event is delayed and weakened compared to FLOWer SST and experimental results. FLOWer and TAU results using the Spalart–Allmaras turbulence model are fairly comparable but in bad agreement with the experiment at the outboard station at r/R=0.77, where they exhibit no dynamic stall at all.
Conference Paper
View Video Presentation: https://doi.org/10.2514/6.2022-2414.vid This paper describes a combined experimental and computational effort to characterize the cycle-to-cycle variations previously observed in oscillating airfoil experiments. It is common in the dynamic stall community to assume that the variation in loads between pitch cycles is primarily due to random turbulent fluctuations, which in turn justifies the assumption that the loads can be accurately represented using simple phase averages. However this work, which numerically and experimentally models an oscillating modified VR-12 airfoil at two different conditions, shows that various aspects ranging from model setup to the inherent fluid dynamics may lead to significant furcation in the loads. These clusters of loads are poorly represented by simple phase averaging techniques and require special consideration. To the best of the authors' knowledge, this work is the first study to successfully capture furcation using CFD and excellent agreement is observed overall for cluster averaged quantities. Furthermore, this work also presents several lessons learned concerning best practices for the dynamic stall community towards improving future correlations between CFD and experimental data and the quality of future dynamic stall datasets in general.
Article
Full-text available
A grid convergence study is performed for the NACA0015 airfoil at static angles of attack, focusing on the onset of stall. Two CFD analyses, elsA and CFL3D, are used for that purpose. Both methods show a large sensitivity to the mesh resolution, and very fine meshes are required in order to reach grid convergence. Both grid-converged solutions under-estimate the flow separation obtained in the experiment. These solutions also significantly differ, especially in terms of boundary layer thickness. Different boundary conditions applied to the transport equations for the turbulent quantities are probably at the source of these differences.
Article
Full-text available
The present work evaluates the potential of a hybrid RANS-LES method to predict the unsteady flow over airfoils in static and oscillating motion. The method implemented (hereafter termed HRLES) blends the k − omega SST RANS model with a localized dynamic ksgs one-equation LES model (LDKM). The unsteady 2D and 3D flow over a NACA 0015 airfoil is computed to evaluate the model performance. The aerodynamic characteristics of the static configuration are in reasonable agreement with experimental results. For the oscillating case, three conditions are simulated: attached flow, mild stall and deep stall. Two-dimensional simulations are conducted for the three dynamic stall conditions, and only the deep stall case is simulated in 3D so far. Overall, the unsteady loads for the attached and mild stall cases show good agreement with experiments. For the mild and the deep stall cases, the HRLES is able to predict flow separation and vortex shedding during the downstroke. In general, these results demonstrate the potential of hybrid methods to correctly simulate complex high Reynolds number flows encountered in aerodynamic applications.
Article
Full-text available
The efficient prediction of helicopter rotor performance, vibratory loads, and aeroelastic properties still relies heavily on the use of comprehensive analysis codes. These comprehensive codes utilize look-up tables to provide two-dimensional aerodynamic characteristics. Typically these tables are comprised of a combination of wind tunnel data, empirical data, and numerical analyses. The potential to rely more heavily on numerical computations based on computational fluid dynamics simulations has become more of a reality with the advent of faster computers and more sophisticated physical models. The ability of five different computational fluid dynamics codes, applied independently, to predict the lift, drag and pitching moments of rotor airfoils is examined for the SC1095 airfoil, which is utilized in the UH-60A main rotor. Extensive comparisons with the results of ten wind tunnel tests are performed. These computational fluid dynamics computations are within experimental data limits for predicting many of the aerodynamic performance characteristics.
Conference Paper
Full-text available
The present paper deals with the definition and application of different unsteady criteria that may be considered in a dedicated aerodynamic design of rotorcraft airfoils. Today’s airfoil design methodologies for rotorcraft applications rely on steady computations and design criteria. Due to the inherent flow unsteadiness at forward flight, caused by variable incoming flow velocity, cyclic pitching as well as blade motion and deformation, it is however deemed necessary to further take into account unsteady aerodynamic effects and characteristics of the airfoil in the design process. Unsteady criteria are introduced for both 2D rotor-environment simulations with varying freestream Mach number and angle of attack and for high-frequency, small amplitude harmonic pitch oscillations at constant Mach number. By means of URANS simulations, with numerical settings validated against experiments, these criteria are exemplarily applied to the OA209 rotor blade airfoil geometry.
Conference Paper
Full-text available
The paper will discuss the latest results of a comprehensive validation activity on the numerical methods TAU and elsA, conducted with respect to dynamic stall applications. The work has been performed in the joint German/French project SIMCOS (Advanced Simulation and Control of Dynamic Stall) in the frame of the DLR/ONERA cooperation on helicopter technologies. The validation was conducted by two-dimensional unsteady RANS simulations on two dynamic stall test cases for the rotor blade airfoil OA209. Test case DS1 measured in the French ONERA-F2 wind tunnel represents a low speed deep dynamic stall case at M = 0.16, Re = 1.8e6, α = 13° ± 5°, and ω* = 0.1 (ω* = 2πfc/v<sub>∞</sub>). Test case DS2 measured in the German DNW-TWG wind tunnel represents a high speed deep dynamic stall case at M = 0.31, Re = 1.16e6, α = 13° ± 7°, and ω* = 0.1. The numerical methods used were the ONERA in-house flow solver elsA and the DLR in-house flow solver TAU. While the elsA code is a structured solver, the TAU code is an unstructured solver using hybrid grids. Simulations were performed with respect to the investigation of the influence of temporal resolution, grid characteristics, turbulence modeling, and transition prediction on the results of the codes. The results of the individual investigations will be discussed and the numerical methods, as well as turbulence and transition modeling from TAU and elsA will be compared.
Article
Full-text available
The efficient prediction of helicopter rotor performance, vibratory loads, and aeroelastic properties still relies heavily on the use of comprehensive analysis codes by the rotorcraft industry. These comprehensive codes utilize look-up tables to provide two-dimensional aerodynamic characteristics. Typically these tables are comprised of a combination of wind tunnel data, empirical data and numerical analyses. The potential to rely more heavily on numerical computations based on Computational Fluid Dynamics (CFD) simulations has become more of a reality with the advent of faster computers and more sophisticated physical models. The ability of five different CFD codes applied independently to predict the lift, drag and pitching moments of rotor airfoils is examined for the SC1095 airfoil, which is utilized in the UH-60A main rotor. Extensive comparisons with the results of ten wind tunnel tests are performed. These CFD computations are found to be as good as experimental data in predicting many of the aerodynamic performance characteristics. Four turbulence models were examined (Baldwin-Lomax, Spalart-Allmaras, Menter SST, and k-omega).
Conference Paper
Full-text available
We focus on multidisciplinary applications of detached-eddy simulation (DES), principally flight mechanics and aeroelasticity. Specifically, the lateral instability (known as abrupt wing stall) of the preproduction F/A-18E is reproduced using DES, including the unsteady shock motion. The presence of low frequency pressure oscillations due to shock motion in the current simulations and the experiments motivated a full aircraft calculation, which showed low frequency high-magnitude rolling moments that could be a significant contributor to the abrupt wing stall phenomenon. DES is also applied to the F-18 high angle of attack research vehicle (HARV) at a moderate angle of attack to reproduce the vortex breakdown leading to vertical stabilizer buffet. Unsteady tail loads are compared to flight test data. This work lays the foundation for future deforming grid calculations to reproduce the aero-elastic tail buffet seen in flight test. Solution based grid adaption is used on unstructured grids in both cases to improve the resolution in the separated region. Previous DoD Challenge work has demonstrated the unique ability of the DES turbulence treatment to accurately and efficiently predict flows with massive separation at flight Reynolds numbers. DES calculations have been performed using the Cobalt code and on unstructured grids, an approach that can deal with complete configurations with very few compromises. A broad range of flows has been examined in previous Challenge work, including aircraft forebodies, airfoil sections, a missile afterbody, vortex breakdown on a delta wing, and the F-16 and F-15E at high angles-of-attack. All DES predictions exhibited a moderate to significant improvement over results obtained using traditional Reynolds-averaged models and often excellent agreement with experimental/flight-test data. DES combines the efficiency of a Reynolds-averaged turbulence model near the wall with the fidelity of Large-Eddy Simulation (LES) in separated regions. Since it uses Large-Eddy Simulation in the separated regions, it is capable of predicting the unsteady motions associated with separated flows. The development and demonstration of improved methods for the prediction of flight mechanics and aeroelasticity in this Challenge is expected to reduce t- he acquisition cost of future military aircraft.
Article
Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.
Conference Paper
This paper presents numerical simulations of the flow around a NACA 0015 airfoil at static and dynamic stall. The treatment of these configurations is a very challenging task for CFD applications. The turbulent flow around the static and in pitch oscillation airfoil is computed using different approaches: 2D RANS, 3D RANS and DES methodologies and with finer and finer meshes in order to try to reach a space converged solution. The main conclusion of the paper is that the prediction of static and all the more dynamic stall is not mature with present modeling capabilities.
Conference Paper
The vortex shedding caused by compressible subsonic flow along a wall cavity has been investigated using a Large-Eddy Simulation (LES)-based turbulence modeling technique that is embedded within a legacy Reynolds-Averaged Navier-Stokes (RANS) solver to assess the improvement in the prediction of the flow field and acoustic of cavity flows beyond the application of classic RANS turbulence models. Numerical simulations applying two-equation Kinetic-Energy Simulation (KES), sub-grid scale hybrid-RANS LES (HRLES-sgs), and Menter k - w shear-stress transport (SST) turbulence methods have been carried out and compared with experiment and LES results. Important frequencies of the flow are determined, illustrating the abilities of advanced turbulence modeling to improve these predictions when compared to RANS models. Evaluation of the influence of the grid, time step and simulation period shows the sensitivity of the predictions to these parameters.
Article
The vortex shedding generated by compressible subsonic flow interacting with a wall cavity has been investigated using large-eddy-simulation-based turbulence techniques embedded within a legacy Reynolds-averaged Navier-Stokes solver. Cavity simulations using hybrid turbulence approaches seek the accuracy of large-eddy simulation by providing filtering and modeling of subgrid-scale turbulence with the cost of traditional Reynolds-averaged Navier-Stokes. Simulations applying differing techniques of hybridization of the Menter k-omega shear stress transport Reynolds-averaged Navier-Stokes approach include detached eddy simulation (DES-SST), blended subgrid-scale turbulence models (GT-HRLES), and a self-adjusting large-eddy-simulation very-large-eddy-simulation technique (KES) provide an understanding of differing hybrid approaches. Cavity flow results from Reynolds-averaged Navier-Stokes and hybrid simulations are compared with experiment and large-eddy simulation predictions. Evaluation of important flow characteristics illustrates the abilities of these advanced turbulence modeling techniques compared with traditional Reynolds-averaged Navier-Stokes models. Examination of the influence of the grid, time step, and simulation period demonstrates the sensitivity of the aerodynamic and aeroacoustic predictions to these parameters. In particular the subgrid-scale blended model, GT-HRLES, shows significant improvement in the ability to capture the acoustic signatures and flowfield features on a Reynolds-averaged Navier-Stokes or very-large-eddy-simulation grid compared with the other models.
Article
Current rotorcraft research to increase flight speed or to alleviate adverse physical phenomena expand the Mach/angle-of-attack envelope in which the rotor blades operate. For example, rotor blades will experience large areas over the rotor disk where reverse-flow effects cannot be neglected during the design and analysis of an efficient rotor at high advance ratios. A cost-effective alternative to extensive experimental analyses is the use of computational fluid dynamics codes to quantify the behavior of airfoils at high and reverse angles of attack, as well as to add to the knowledge of the behavior of airfoils when they are immersed in these flows. Numerical experiments have been performed with correlation to experimental databases that examine the ability of computational fluid dynamics to accurately model airfoil characteristics at these angles of attack. It is observed that the use of recently developed hybrid Reynolds-averaged Navier-Stokes and large-eddy simulation turbulence methods result in a significant improvement in the ability of computational fluid dynamics to predict the characteristics of airfoils in these angle-of-attack regimes. Modeling of the airfoil trailing edge is more sensitive when reverse-flow angles of attack are considered.
Article
The accuracy and efficiency of two different types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18%-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. For both explicit and implicit algorithms, nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time subiterations (dual time stepping). Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.
Article
This paper describes the CFD activities achieved by ONERA during the first year of an internal multidisciplinary project on dynamic stall. The numerical simulations have been performed for a NACA0015 airfoil in stall conditions. These activities concern the efficiency of numerical methods, the accuracy of turbulence models and the influence of the grid resolution. The problem of stall was widely studied in many previous works but unfortunately it clearly appears that state-of-the-art CFD, which is most of the time considered as mature for such kind of application in the published literature, is far from our expectations. In this context, we have chosen to start from the beginning by considering static stall, where a grid convergence study is been performed. Although very fine grids have been used up to now, the solution still shows grid dependency more especially in the outer edge of the boundary layer.
Article
Earlier experiments have documented the onset of compressible dynamic stall either from the bursting of a leading-edge laminar separation bubble or from a leading-edge shock, depending on the Reynolds number and Mach number. For certain combinations of conditions, the supersonic flow and the bubble dynamics compete with each other. The consequent complex interactions lead to a discovered mechanism of dynamic stall onset. Details of these various mechanisms are discussed.
Article
An unfactored implicit tine-marching method for the solution of the unsteady two-dimensional Euler equations on deforming grids is described. The present work is placed into a multiblock framework and fits into the development of a generally applicable parallel multiblock how solver. The convective terms are discretized using an upwind total variation diminishing scheme, whereas the unsteady governing equations are discretized using an implicit dual-time approach. The large sparse linear system arising from the implicit time discretization at each pseudotime step is solved efficiently by using a conjugate-gradient-type method with a preconditioning based on. a block incomplete lower-upper factorization. Results are shown for a series of pitching airfoil test cases selected. from the AGARD aeroelastic configurations for the NACA 0012 airfoil. Comparisons with experimental data and previous published results are presented. The efficiency of the method is demonstrated by looking at the effect of a number of numerical parameters, such as the conjugate gradient tolerance and the size of the global time step and by carrying out a grid refinement study. Finally, a demonstration test case for the Williams airfoil(Williams, B. R., "An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils:" National Physical Lab., Aeronautical Research Council, Research Memorandum 3717, London, 1973) with an oscillating flap is presented, highlighting the capability of the grid deformation technique.
Article
A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. In order to improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction were investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low speed and high speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart-Allmaras-type models to state-of-the-art seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.
Article
In this work, the effect of wall interference on steady and oscillating airfoils in a subsonic wind tunnel is studied. A variety of approaches including linear theory, compressible inviscid and viscous computations, and experimental data are considered. Integral transform solutions of the linearized potential equations show an augmentation of the lift magnitude for steady flows when the wall is close to the airfoil surface. For oscillating airfoils, lift augmentation is accompanied by a significant change in the phase of the lift response. Idealized compressible Euler calculations are seen to corroborate the linear theory under conditions that are sufficiently away from acoustic resonance. Further, the theory compares well with compressible Reynolds-averaged Navier-Stokes calculations and experimental measurements over a wide range of attached flows at subsonic Mach numbers. The present methodology can thus be used to predict wall interference effects and also to help extrapolate linear and nonlinear (dynamic stall) wind tunnel data to free-air conditions.
Article
The static and dynamic characteristics of seven helicopter sections and a fixed-wing supercritical airfoil were investigated over a wide range of nominally two dimensional flow conditions, at Mach numbers up to 0.30 and Reynolds numbers up to 4 x 10 to the 6th power. Details of the experiment, estimates of measurement accuracy, and test conditions are described in this volume (the first of three volumes). Representative results are also presented and comparisons are made with data from other sources. The complete results for pressure distributions, forces, pitching moments, and boundary-layer separation and reattachment characteristics are available in graphical form in volumes 2 and 3. The results of the experiment show important differences between airfoils, which would otherwise tend to be masked by differences in wind tunnels, particularly in steady cases. All of the airfoils tested provide significant advantages over the conventional NACA 0012 profile. In general, however, the parameters of the unsteady motion appear to be more important than airfoil shape in determining the dynamic-stall airloads.
Article
Several issues relating to the application of Chimera overlapped grids to complex geometries and flowfields are discussed. These include the addition of geometric components with different grid topologies, gridding for intersecting pieces of geometry, and turbulence modeling in grid overlap regions. Sample results are presented for transonic flow about the Space Shuttle launch vehicle. Comparisons with wind tunnel and flight measured pressures are shown.
Article
Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-omega model of Wilcox In the inner region of the boundary layer and switches to the standard k -epsilon model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity. The second model results from a modification to the definition of the eddy-viscosity in the BSL model, which accounts for the effect of the transport of the principal turbulent shear stress. The new model is called the shear-stress transport-model and leads to major improvements in the prediction of adverse pressure gradient flows.
Time accuracy and the use of implicit methods In: 11th Computational fluid dynamics conference, AIAA 1993-3360
  • T Pulliam
Pulliam T. Time accuracy and the use of implicit methods. In: 11th Computational fluid dynamics conference, AIAA 1993-3360, Orlando, FL; July 6–9, 1993.
Stokes simulation of wing tip and wing juncture interactions for a pitching wing In: AIAA 1994-2259, 25th fluid dynamics conference
  • R Newsome
  • Navier
Newsome R. Navier–Stokes simulation of wing tip and wing juncture interactions for a pitching wing. In: AIAA 1994-2259, 25th fluid dynamics conference, Colorado Springs, CO; June 20–23, 1994.
Numerical investigation of laminar/ turbulent transition effects on the dynamic stall of an oscillating airfoil
  • M Costes
  • V Gleize
  • Le Pape
  • A Richez
Costes M, Gleize V, Le Pape A, Richez F. Numerical investigation of laminar/ turbulent transition effects on the dynamic stall of an oscillating airfoil. In: AHS specialists conference on aerodynamics, vol. 2. San Francisco, California; January 23-25, 2008. p. 761-82.
Multidisciplinary applications of detached-eddy simulation to separated flows at high Reynolds numbers. In: Proceedings of the department of defense high performance computing modernization program users group conference
  • Morton S M Steenman
  • Cummings R J Forsythe
  • E Wurtzler
  • K Squires
Morton S, Steenman M, Cummings R, Forsythe J, Wurtzler E, Squires K, et al. Multidisciplinary applications of detached-eddy simulation to separated flows at high Reynolds numbers. In: Proceedings of the department of defense high performance computing modernization program users group conference; June, 2004. p. 103–11.
Zonal hybrid RANS–LES method for static and oscillating airfoils and wings. In: Collection of technical papers – 44th AIAA aerospace sciences meeting
  • Kirtas M M Sanchez-Rocha
  • Menon
Sanchez-Rocha M, Kirtas M, Menon S. Zonal hybrid RANS–LES method for static and oscillating airfoils and wings. In: Collection of technical papers – 44th AIAA aerospace sciences meeting, AIAA 2006-1256, Reno, NV, vol. 20; 2006. p. 15211–15231.
The prediction and validation of static and dynamic stall, In: Paper T221, Presented at Heli Japan
  • Ma Mouton
  • Smith
  • Mj
Mouton MA, Smith MJ. The prediction and validation of static and dynamic stall, In: Paper T221, Presented at Heli Japan 2010, Saitama, Japan; November 13, 2010.
Modeling and analysis of the physics of flapped airfoils and wings. PhD dissertation, Georgia Institute of Technology
  • Nd Liggett
Liggett ND. Modeling and analysis of the physics of flapped airfoils and wings. PhD dissertation, Georgia Institute of Technology; July, 2012. 156 N.D. Liggett, M.J. Smith / Computers & Fluids 66 (2012) 140–156
Numerical and physical analysis of the turbulent viscous flow around a NACA0015 profile at stall. In: European congress on computational methods in applied sciences and engineering
  • V Gleize
  • J Szydlowski
  • M Costes
Gleize V, Szydlowski J, Costes M. Numerical and physical analysis of the turbulent viscous flow around a NACA0015 profile at stall. In: European congress on computational methods in applied sciences and engineering, Jyvaskyla, Finland; July 24–28, 2004.
Time accuracy and the use of implicit methods
  • T Pulliam
Pulliam T. Time accuracy and the use of implicit methods. In: 11th Computational fluid dynamics conference, AIAA 1993-3360, Orlando, FL; July 6-9, 1993.
Zonal hybrid RANS-LES method for static and oscillating airfoils and wings
  • M Sanchez-Rocha
  • M Kirtas
  • S Menon
Sanchez-Rocha M, Kirtas M, Menon S. Zonal hybrid RANS-LES method for static and oscillating airfoils and wings. In: Collection of technical papers -44th AIAA aerospace sciences meeting, AIAA 2006-1256, Reno, NV, vol. 20; 2006. p. 15211-15231.
Application of the chimera overlapped grid scheme to simulation of space shuttle ascent flows
  • P Buning
  • S Parks
  • W Chan
  • K Renze
Buning P, Parks S, Chan W, Renze K. Application of the chimera overlapped grid scheme to simulation of space shuttle ascent flows. In: Proceedings of the 4th international symposium on computational fluid dynamics, vol. 1. Davis (California);
The prediction and validation of static and dynamic stall
  • M A Mouton
  • M J Smith
Mouton MA, Smith MJ. The prediction and validation of static and dynamic stall, In: Paper T221, Presented at Heli Japan 2010, Saitama, Japan; November 13, 2010.
Modeling and analysis of the physics of flapped airfoils and wings
  • N D Liggett
Liggett ND. Modeling and analysis of the physics of flapped airfoils and wings. PhD dissertation, Georgia Institute of Technology; July, 2012.